Tag: entropy

• Dispelling Maxwell’s demon

  Maxwell’s demon is one of the most famous thought experiments in the history of physics, a puzzle first posed in the 1860s that continues to shape scientific debates to this day. I’ve struggled to make sense of it for years. Last week I had some time and decided to hunker down and figure it out, and I think I succeeded. The following post describes the fruits of my efforts.

  At first sight, the Maxwell’s demon paradox seems odd because it presents a supernatural creature tampering with molecules of gas. But if you pare down the imagery and focus on the technological backdrop of the time of James Clerk Maxwell, who proposed it, a profoundly insightful probe of the second law of thermodynamics comes into view.

  The thought experiment asks a simple question: if you had a way to measure and control molecules with perfect precision and at no cost, will you able to make heat flow backwards, as if in an engine?

  Picture a box of air divided into two halves by a partition. In the partition is a very small trapdoor. It has a hinge so it can swing open and shut. Now imagine a microscopic valve operator that can detect the speed of each gas molecule as it approaches the trapdoor, decide whether to open or close the door, and actuate the door accordingly.

  The operator follows two simple rules: let fast molecules through from left to right and let slow molecules through from right to left. The temperature of a system is nothing but the average kinetic energy of its constituent particles. As the operator operates, over time the right side will heat up and the left side will cool down — thus producing a temperature gradient for free. Where there’s a temperature gradient, it’s possible to run a heat engine. (The internal combustion engine in fossil-fuel vehicles is a common example.)

  

  But the possibility that this operator can detect and sort the molecules, thus creating the temperature gradient without consuming some energy of its own, seems to break the second law of thermodynamics. The second law states that the entropy of a closed system increases over time — whereas the operator ensures that the temperature will decrease, violating the law. This was the Maxwell’s demon thought experiment, with the demon as a whimsical stand-in for the operator.

  The paradox was made compelling by the silent assumption that the act of sorting the molecules could have no cost — i.e. that the imagined operator didn’t add energy to the system (the air in the box) but simply allowed molecules that are already in motion to pass one way and not the other. In this sense the operator acted like a valve or a one-way gate. Devices of this kind — including check valves, ratchets, and centrifugal governors — were already familiar in the 19th century. And scientists assumed that if they were scaled down to the molecular level, they’d be able to work without friction and thus separate hot and cold particles without drawing more energy to overcome that friction.

  This detail is in fact the fulcrum of the paradox, and the thing that’d kept me all these years from actually understanding what the issue was. Maxwell et al. assumed that it was possible that an entity like this gate could exist: one that, without spending energy to do work (and thus increase entropy), could passively, effortlessly sort the molecules. Overall, the paradox stated that if such a sorting exercise really had no cost, the second law of thermodynamics would be violated.

  The second law had been established only a few decades before Maxwell thought up this paradox. If entropy is taken to be a measure of disorder, the second law states that if a system is left to itself, heat will not spontaneously flow from cold to hot and whatever useful energy it holds will inevitably degrade into the random motion of its constituent particles. The second law is the reason why perpetual motion machines are impossible, why the engines in our cars and bikes can’t be 100% efficient, and why time flows in one specific direction (from past to future).

  Yet Maxwell’s imagined operator seemed to be able to make heat flow backwards, sifting molecules so that order increases spontaneously. For many decades, this possibility challenged what physicists thought they knew about physics. While some brushed it off as a curiosity, others contended that the demon itself must expend some energy to operate the door and that this expense would restore the balance. However, Maxwell had been careful when he conceived the thought experiment: he specified that the trapdoor was small and moved without friction, so it could in principle operate in a negligible way. The real puzzle lay elsewhere.

  In 1929, the Hungarian physicist Leó Szilard sharpened the problem by boiling it down to a single-particle machine. This so-called Szilard engine imagined one gas molecule in a box with a partition that could be inserted or removed. By observing on which side the molecule lay and then allowing it to push a piston, the operator could apparently extract work from a single particle at uniform temperature. Szilard showed that the key step was not the movement of the piston but the acquisition of information: knowing where the particle was. That is, Szilard reframed the paradox to be not about the molecules being sorted but about an observer making a measurement.

  (Aside: Szilard was played by Máté Haumann in the 2023 film Oppenheimer.)

  

  The next clue to cracking the puzzle came in the mid-20th century from the growing field of information theory. In 1961, the German-American physicist Rolf Landauer proposed a principle that connected information and entropy directly. Landauer’s principle states that while it’s possible in principle to acquire information in a reversible way — i.e. to be able to acquire it as well as lose it — erasing information from a device with memory has a non-zero thermodynamic cost that can’t be avoided. That is, the act of resetting a memory register of one bit to a standard state generates a small amount of entropy (proportional to Boltzmann’s constant multiplied by the logarithm of two).

  The American information theorist Charles H. Bennett later built on Landauer’s principle and argued that Maxwell’s demon could gather information and act on it — but in order to continue indefinitely, it’d have to erase or overwrite its memory. And that this act of resetting would generate exactly the entropy needed to compensate for the apparent decrease, ultimately preserving the second law of thermodynamics.

  Taken together, Maxwell’s demon was defeated not by the mechanics of the trapdoor but by the thermodynamic cost of processing information. Specifically, the decrease in entropy as a result of the molecules being sorted by their speed is compensated for by the increase in entropy due to the operator’s rewriting or erasure of information about the molecules’ speed. Thus a paradox that’d begun as a challenge to thermodynamics ended up enriching it — by showing information could be physical. It also revealed to scientists that entropy is disorder in matter and energy as well as is linked to uncertainty and information.

  Over time, Maxwell’s demon also became a fount of insight across multiple branches of physics. In classical thermodynamics, for example, entropy came to represent a measure of the probabilities that the system could exist in different combinations of microscopic states. That is, the probabilities referred to the likelihood that a given set of molecules could be arranged in one way instead of another. In statistical mechanics, Maxwell’s demon gave scientists a concrete way to think about fluctuations. In any small system, random fluctuations can reduce entropy for some time in a small portion. While the demon seemed to exploit these fluctuations, the laws of probability were found to ensure that on average, entropy would increase. So the demon became a metaphor for how selection based on microscopic knowledge could alter outcomes but also why such selection can’t be performed without paying a cost.

  

  For information theorists and computer scientists, the demon was an early symbol of the deep ties between computation and thermodynamics. Landauer’s principle showed that erasing information imposes a minimum entropy cost — an insight that matters for how computer hardware should be designed. The principle also influenced debates about reversible computing, where the goal is to design logic gates that don’t ever erase information and thus approach zero energy dissipation. In other words, Maxwell’s demon foreshadowed modern questions about how energy-efficient computing could really be.

  Even beyond physics, the demon has seeped into philosophy, biology, and social thought as a symbol of control and knowledge. In biology, the resemblance between the demon and enzymes that sorts molecules has inspired metaphors about how life maintains order. In economics and social theory, the demon has been used to discuss the limits of surveillance and control. The lesson has been the same in every instance: that information is never free and that the act of using it imposes inescapable energy costs.

  I’m particularly taken by the philosophy that animates the paradox. Maxwell’s demon was introduced as a way to dramatise the tension between the microscopic reversibility of physical laws and the macroscopic irreversibility encoded in the second law of thermodynamics. I found that a few questions in particular — whether the entropy increase due to the use of information is a matter of an observer’s ignorance (i.e. because the observer doesn’t know which particular microstate the system occupies at any given moment), whether information has physical significance, and whether the laws of nature really guarantee the irreversibility we observe — have become touchstones in the philosophy of physics.

  In the mid-20th century, the Szilard engine became the focus of these debates because it refocused the second law from molecular dynamics to the cost of acquiring information. Later figures such as the French physicist Léon Brillouin and the Hungarian-Canadian physicist Dennis Gabor claimed that it’s impossible to measure something without spending energy. Critics however countered that these requirements stipulated the need for specific technologies that would in turn smuggle in some limitations — rather than stipulate the presence of a fundamental principle. That is to say, the debate among philosophers became whether Maxwell’s demon was prevented from breaking the second law by deep and hitherto hidden principles or by engineering challenges.

  This gridlock was broken when physicists observed that even a demon-free machine must leave some physical trace of its interactions with the molecule. That is, any device that sorts particles will end up in different physical states depending on the outcome, and to complete a thermodynamic cycle those states must be reset. Here, the entropy is not due to the informational content but due to the logical structure of memory. Landauer solidified this with his principle that logically irreversible operations such as erasure carry a minimum thermodynamic cost. Bennett extended this by saying that measurements can be made reversibly but not erasure. The philosophical meaning of both these arguments is that entropy increase isn’t just about ignorance but also about parts of information processing being irreversible.

  

  In the quantum domain, the philosophical puzzles became more intense. When an object is measured in quantum mechanics, it isn’t just about an observer updating the information they have about the object — the act of measuring also seems to alter the object’s quantum states. For example, in the Schrödinger’s cat thought experiment, checking whether there’s a cat in the box also causes the cat to default to one of two states: dead or alive. Quantum physicists have recreated Maxwell’s demon in new ways in order to check whether the second law continues to hold. And over the course of many experiments, they’ve concluded that indeed it does.

  The second law didn’t break even when Maxwell’s demon could exploit phenomena that aren’t available in the classical domain, including quantum entanglement, superposition, and tunnelling. This was because, among others, quantum mechanics also has some restrictive rules of its own. For one, some physicists have tried to design “quantum demons” that use quantum entanglement between particles to sort them without expending energy. But these experiments have found that as soon as the demon tries to reset its memory and start again, it must erase the record of what happened before. This step destroys the advantage and the entropy cost returns. The overall result is that even a “quantum demon” gains nothing in the long run.

  For another, the no-cloning theorem states that you can’t make a perfect copy of an unknown quantum state. If the demon could freely copy every quantum particle it measured, it could retain flawless records while still resetting its memory, this avoiding the usual entropy cost. The theorem blocks this strategy by forbidding perfect duplication, ensuring that information can’t be ‘multiplied’ without limit. Similarly, the principle of unitarity implies that a system will always evolve in a way that preserves overall probabilities. As a result, quantum phenomena can’t selectively amplify certain outcomes while discarding others. For the demon, this means it can’t secretly limit the range of possible states the system can occupy into a smaller set where the system has lower entropy, because unitarity guarantees that the full spread of possibilities is preserved across time.

  All these rules together prevent the demon from multiplying or rearranging quantum states in a way that would allow it to beat the second law.

  Then again, these ‘blocks’ that prevent Maxwell’s demon from breaking the second law of thermodynamics in the quantum realm raise a puzzle of their own: is the second law of thermodynamics guaranteed no matter how we interpret quantum mechanics? ‘Interpreting quantum mechanics’ means to interpret what the rules of quantum mechanics say about reality, a topic I covered at length in a recent post. Some interpretations say that when we measure a quantum system, its wavefunction “collapses” to a definite outcome. Others say collapse never happens and that measurement is just entangled with the environment, a process called decoherence. The Maxwell’s demon thought experiment thus forces the question: is the second law of thermodynamics safe in a particular interpretation of quantum mechanics or in all interpretations?

  

  Landauer’s idea, that erasing information always carries a cost, also applies to quantum information. Even if Maxwell’s demon used qubits instead of bits, it won’t be able to escape the fact that to reuse its memory, it must erase the record, which will generate heat. But then the question becomes more subtle in quantum systems because qubits can be entangled with each other, and their delicate coherence — the special quantum link between quantum states — can be lost when information is processed. This means scientists need to carefully separate two different ideas of entropy: one based on what we as observers don’t know (our ignorance) and another based on what the quantum system itself has physically lost (by losing coherence).

  The lesson is that the second law of thermodynamics doesn’t just guard the flow of energy. In the quantum realm it also governs the flow of information. Entropy increases not only because we lose track of details but also because the very act of erasing and resetting information, whether classical or quantum, forces a cost that no demon can avoid.

  Then again, some philosophers and physicists have resisted the move to information altogether, arguing that ordinary statistical mechanics suffices to resolve the paradox. They’ve argued that any device designed to exploit fluctuations will be subject to its own fluctuations, and thus in aggregate no violation will have occurred. In this view, the second law is self-sufficient and doesn’t need the language of information, memory or knowledge to justify itself. This line of thought is attractive to those wary of anthropomorphising physics even if it also risks trivialising the demon. After all, the demon was designed to expose the gap between microscopic reversibility and macroscopic irreversibility, and simply declaring that “the averages work out” seems to bypass the conceptual tension.

  Thus, the philosophical significance of Maxwell’s demon is that it forces us to clarify the nature of entropy and the second law. Is entropy tied to our knowledge/ignorance of microstates, or is it ontic, tied to the irreversibility of information processing and computation? If Landauer is right, handling information and conserving energy are ‘equally’ fundamental physical concepts. If the statistical purists are right, on the other hand, then information adds nothing to the physics and the demon was never a serious challenge. Quantum theory can further stir both pots by suggesting that entropy is closely linked to the act of measurement, of quantum entanglement, and how quantum systems ‘collapse’ to classical ones by the process of decoherence. The demon debate therefore tests whether information is a physically primitive entity or a knowledge-based tool. Either way, however, Maxwell’s demon endures as a parable.

  Ultimately, what makes Maxwell’s demon a gift that keeps giving is that it works on several levels. On the surface it’s a riddle about sorting molecules between two chambers. Dig a little deeper and it becomes a probe into the meaning of entropy. If you dig even further, it seems to be a bridge between matter and information. As the Schrödinger’s cat thought experiment dramatised the oddness of quantum superposition, Maxwell’s demon dramatised the subtleties of thermodynamics by invoking a fantastical entity. And while Schrödinger’s cat forces us to ask what it means for a macroscopic system to be in two states at once, Maxwell’s demon forces us to ask what it means to know something about a system and whether that knowledge can be used without consequence.

  2025.09.19

• Quantum clock breaks entropy barrier

  In physics, the second law of thermodynamics says that a closed system tends to become more disordered over time. This disorder is captured in an entity called entropy. Many devices, especially clocks, are affected by this law because they need to tick regularly to measure time. But every tick creates a bit of disorder, i.e. increases the entropy, and physicists have believed for a long time now that this places a fundamental limit on how precise a clock can be. The more precise you want your clock, the more entropy (and thus more energy) you’ll have to expend.

  A study published in Nature Physics on June 2 challenges this wisdom. In it, researchers from Austria, Malta, and Sweden asked if the second law of thermodynamics really set a limit on a clock’s precision and came away, surprisingly, with a design of a new kind of quantum clock that’s too precise scientists once believed possible for the amount of energy it spends to achieve that precision.

  The researchers designed this clock using a spin chain. Imagine a ring made of several quantum sites, like minuscule cups. Each cup can hold an excitation — say, a marble that can hop from cup to cup. This excitation moves around the ring and every time it completes a full circle, the clock ticks once. A spin chain is, broadly speaking, a series of connected quantum systems (the sites) arranged in a ring and the excitation is a subatomic particle or packet of energy that moves from site to site.

  In most clocks, every tick is accompanied by the dissipation of some energy and a small increase in entropy. But in the model in the new study, only the last link in the circle, where the last quantum system was linked to the first one, dissipated energy. Everywhere else, the excitation moved without losing energy, like a wave gliding smoothly around the ring. The movement of the excitation in this lossless way through most of the ring is called coherent transport.

  The researchers used computer simulations to help them adjust the hopping rates — or how easily the excitation moved between sites — and thus to make the clock as precise as possible. They found that the best setup involved dividing the ring into three regions: (i) in the preparation ramp, the excitation was shaped into a wave packet; (ii) in the bulk propagation phase, the wave packet moved steadily through the ring; and (iii) in the boundary matching phase, the wave packet was reset for the next tick.

  The team measured the clock’s precision as the number of ticks it completed before it was one tick ahead or behind a perfect clock. Likewise, team members defined the entropy per tick to be the amount of energy dissipated per tick. Finally, the team compared this quantum clock to classical clocks and other quantum models, which typically show a linear relationship between precision and entropy: e.g. if the precision doubled, the entropy doubled as well.

  The researchers, however, found that the precision of their quantum clock grew exponentially with entropy. In other words, if the amount of entropy per tick increased only slightly, the precision increased by a big leap. It was proof that, at least in principle, it’s possible to build a clock to be arbitrarily precise while keeping the system’s entropy down, all without falling afoul of the second law.

  That is, contrary to what many physicists thought, the second law of thermodynamics doesn’t strictly limit a clock precision, at least not for quantum clocks like this one. The clock’s design allowed it to sidestep the otherwise usual trade-off between precision and entropy.

  During coherent transport, the process is governed only by the system’s Hamiltonian, i.e. the rules for how energy moves in a closed quantum system. In this regime, the excitation acts like a wave that spreads smoothly and reversibly, without losing any energy or creating any disorder. Imagine a ball rolling on a perfectly smooth, frictionless track. It keeps moving without slowing down or heating up the track. Such a thing is impossible in classical mechanics, like in the ball example, but it’s possible in quantum systems. The tradeoff of course is that the latter are very small and very fragile and thus harder to manipulate.

  In the present study, the researchers have proved that it’s possible to build a quantum clock that takes advantage of coherent transport to tick while dissipating very little energy. Their model, the spin chain, uses a Hamiltonian that only allows the excitation to coherently hop to its nearest neighbour. The researchers engineered the couplings between the sites in the preparation ramp part of the ring to shape the excitation into a traveling wave packet that moves predominantly in the forward direction.

  This tendency to move in only direction is further bolstered at the last link, where the last site is coupled to the first. Here, the researchers installed a thermal gradient — a small temperature difference that encouraged the wave to restart its journey rather than be reflected and move backwards through the ring. When the excitation crossed this thermodynamic bias, the clock ticked once and also dissipated some energy.

  Three points here. First, remember that this is a quantum system. The researchers are dealing with energy (almost) at its barest, manipulating it directly without having to bother with an accoutrement of matter covering it. In the classical regime, such accoutrements are unavoidable. For example, if you have a series of cups and you want to make an excitation hop through it, you do so with a marble. But while the marble contains the (potential) energy that you want to move through the cups, it also has mass and it dissipates energy whenever it hops into a cup, e.g. it might bounce when it lands and it will release sound when it strikes the cup’s material. So while the marble metaphor earlier might have helped you visualise the quantum clock, remember that the metaphor has limitations.

  Second, for the quantum clock to work as a clock, it needs to break time-reversal symmetry (a concept I recently discussed in the context of quasicrystals). Say you remove the thermodynamic bias at the last link of the ring and replace it with a regular link. In this case the excitation will move randomly — i.e. at each step it will randomly pick the cup to move to, forward or backward, and keep going. If you reversed time, the excitation’s path will still be random and just evolve in reverse.

  However, the final thermodynamically biased link causes the excitation to acquire a preference for moving in one direction. The system thus breaks time-reversal symmetry because even if you reverse the flow of time, the system will encourage the excitation to move in one direction and one direction only. This in turn is essential for the quantum system to function like a clock. That is, the excitation needs to traverse a fixed number of cups in the spin chain and then start from the first cup. Only between these two stages will the system count off a ‘tick’. Breaking time-reversal symmetry thus turns the device into a clock.

  Three, the thermodynamic bias ensures that the jump from the last site to the first is more likely than the reverse, and the entropy is the cost the system pays in order to ensure the jump. Equally, the greater the thermodynamic bias, the more likely the excitation is to move in one direction through spin chain as well as make the jump in the right direction at the final step. Thus, the greater the thermodynamic bias, the more precise the clock will be.

  The new study excelled by creating a sufficiently precise clock while minimising the entropy cost.

  According to the researchers, its design design could help build better quantum clocks, which are important for quantum computers, quantum communication, and to make ultra-precise precise measurements of the kind demanded by atomic clocks. The clock’s ticks could also be used to emit single photons at regular intervals — a technology increasingly in demand for its use in quantum networks of the sort China, the US, and India are trying to build.

  But more fundamentally, the clock’s design — which confines energy dissipation to a single link and uses coherent transport everywhere else — and that design’s ability to evade the precision-entropy trade-off challenges a longstanding belief that the second law of thermodynamics strictly limits precision.

  Featured image credit: Meier, F., Minoguchi, Y., Sundelin, S. et al. Nat. Phys. (2025).

  2025.07.12

• Why do quasicrystals exist?

  Featured image: An example of zellij tilework in the Al Attarine Madrasa in Fes, Morocco (2012), with complex geometric patterns on the lower walls and a band of calligraphy above. Caption and credit: just_a_cheeseburger (CC BY)

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  ‘Quasi’ means almost. It’s an unfair name for quasicrystals. These crystals exist in their own right. Their name comes from the internal arrangement of their atoms. A crystal is made up of a repeating group of some atoms arranged in a fixed way. The smallest arrangement that repeats to make up the whole crystal is called the unit cell. In diamond, a convenient unit cell is four carbon atoms bonded to each other in a tetrahedral (pyramid-like) arrangement. Millions of copies of this unit cell together make up a diamond crystal. The unit cell of sodium chloride has a cubical shape: the chloride ions (Cl^–) occupy the corners and face centres while the sodium ions (Na⁺) occupy the middle of the edges and centre of the cube. As this cube repeats itself, you get table salt.

  The structure of all crystals thus follows two simple rules: have a unit cell and repeat it. Thus the internal structure of crystals is periodic. For example if a unit cell is 5 nanometres wide, it stands to reason you’ll see the same arrangement of atoms after every 5 nm. And because it’s the same unit cell in all directions and they don’t have any gaps between them, the unit cells fill the space available. It’s thus an exercise in tiling. For example, you can cover a floor of any shape completely with square or triangular tiles (you’ll just need to trim those at the edges). But you can’t do this with pentagonal tiles. If you do, the tiles will have gaps between them that other pentagonal tiles can’t fill.

  Quasicrystals buck this pattern in a simple way: their unit cells are like pentagonal tiles. They repeat themselves but the resulting tiling isn’t periodic. There are no gaps in the crystal either because instead of each unit cell just like the one on its left or right, the tiles sometimes slot themselves in by rotating by an angle. Thus rather than the crystal structure following a grid-like pattern, the unit cells seem to be ordered along curves. As a result, even though the structure may have an ordered set of atoms, it’s impossible to find a unit cell that by repeating itself in a straight line gives rise to the overall crystal. In technical parlance, the crystal is said to lack translational symmetry.

  Such structures are called quasicrystals. They’re obviously not crystalline, because they lack a periodic arrangement of atoms. They aren’t amorphous either, like the haphazardly arranged atoms of glass. Quasicrystals are somewhere in between: their atoms are arranged in a fixed way, with different combinations of pentagonal, octagonal, and other tile shapes that are disallowed in regular crystals, and with the substance lacking a unit cell. Instead the tiles twist and turn within the structure to form mosaic patterns like the ones featured in Islamic architecture (see image at the top).

  

  The discovery of quasicrystals in the early 1980s was a revolutionary moment in the history of science. It shook up what chemists believed a crystal should look like and what rules the unit cell ought to follow. The first quasicrystals that scientists studied were made in the lab, in particular aluminium-manganese alloys, and there was a sense that these unusual crystals didn’t occur in nature. That changed in the 1990s and 2000s when expeditions to Siberia uncovered natural quasicrystals in meteorites that had smashed into the earth millions of years ago. But even this discovery kept one particular question about quasicrystals alive: why do they exist? Both Al-Mn alloys and the minerals in meteorites form in high temperatures and extreme pressures. The question of their existence, more than just because they can, is a question about whether the atoms involved are forced to adopt a quasicrystal rather than a crystal structure. In other words, it asks if the atoms would rather adopt a crystal structure but don’t because their external conditions force them not to.

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  This post benefited from feedback from Adhip Agarwala.

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  Often a good way to understand the effects of extreme conditions on a substance is using the tools of thermodynamics — the science of the conditions in which heat moves from place to another. And in thermodynamics, the existential question can be framed like this, to quote from a June paper in Nature Physics: “Are quasicrystals enthalpy-stabilised or entropy-stabilised?” Enthalpy-stabilised means the atoms of a quasicrystal are arranged in a way where they collectively have the lowest energy possible for that group. It means the atoms aren’t arranged in a less-than-ideal way forced by their external conditions but because the quasicrystal structure in fact is better than a crystal structure. It answers “why do quasicrystals exist?” with “because they want to, not just because they can”. Entropy-stabilised goes the other way. That is: at 0 K (-273.15º C), the atoms would rather come together as a crystal because a crystal structure has lower energy at absolute zero. But as the temperature increases, the energy in the crystal builds up and forces the atoms to adjust where they’re sitting so that they can accommodate new forces. At some higher temperature, the structure becomes entropy-stabilised. That is, there’s enough disorder in the structure — like sound passing through the grid of atoms and atoms momentarily shifting their positions — that allows it to hold the ‘excess’ energy but at the same time deviate from the orderliness of a crystal structure. Entropy stabilisation answers “why do quasicrystals exist?” with “because they’re forced to, not because they want to”.

  In materials science, the go-to tool to judge whether a crystal structure is energetically favourable is density functional theory (DFT). It estimates the total energy of a solid and from there scientists can compare competing phases and decide which one is most stable. If four atoms will have less energy arranged as a cuboid than as a pyramid at a certain temperature and pressure, then the cuboidal phase is said to be more favoured. The problem is DFT can’t be directly applied to quasicrystals because the technique assumes that a given mineral has a periodic internal structure. Quasicrystals are aperiodic. But because scientists are already comfortable with using DFT, they have tried to surmount this problem by considering a superunit cell that’s made up of a large number of atoms or by assuming that a quasicrystal’s structure, while being aperiodic in three dimensions, could be periodic in say four dimensions. But the resulting estimates of the solid’s energy have not been very good.

  In the new Nature Physics paper, scientists from the University of Michigan, Ann Arbor, have reported a way around the no-unit-cell problem to apply DFT to estimate the energy of two quasicrystals. And they found that these quasicrystals are enthalpy-stabilised. The finding answer is a chemistry breakthrough because it raises the possibility of performing DFT in crystals without translational symmetry. Further, by showing that two real quasicrystals are enthalpy-stabilised, chemists may be forced to rethink why almost every other inorganic material does adopt a repeating structure. Crystals are no longer at the centre of the orderliness universe.

  

  The team started by studying the internal structure of two quasicrystals using X-rays, then ‘scooped’ out five random parts for further analysis. Each of these scoops had 24 to 740 atoms. Second, the team used a modified version of DFT called DFT-FE. The computational cost of running DFT scales increases according to the cube of the number of atoms being studied. If studying four atoms with DFT requires X amount of computing power, 24 atoms would require 8,000 times X and 740 atoms would require 400 million times X. Instead the computational cost of DFT-FE scales as the square of the number of atoms, which makes a big difference. Continuing from the previous example, 24 atoms would require 400 times X and 740 atoms would require half a million times X. But the lower computational cost of DFT-FE is still considerable. The researchers’ solution was to use GPUs — the processors originally developed to run complicated video games and today used to run artificial intelligence (AI) apps like ChatGPT.

  The team was able to calculate that the resulting energy estimates for a quasicrystal was off by no more than 0.3 milli-electron-volt (meV) per atom, considered acceptable. They also applied their technique to a known crystal, ScZn₆, and confirmed that its estimate of the energy matched the known value (5-9 meV per atom). They were ready to go now.

  When they applied DFT-FE to scandium-zinc and ytterbium-cadmium quasicrystals, they found clear evidence that they were enthalpy-stabilised. Each atom in the scandium-zinc quasicrystal had 23 meV less energy than if it had been part of a crystal structure. Similarly atoms in the ytterbium-cadmium quasicrystal had roughly 7 meV less each. The verdict was obvious: translational symmetry is not required for the most stable form of an inorganic solid.

  

  The researchers also explored why the ytterbium-cadmium quasicrystal is so much easier to make than the scandium-zinc quasicrystal. In fact the former was the world’s first two-element quasicrystal to be discovered, 25 years ago this year. The team broke down the total energy as the energy in the bulk plus energy on the surface, and found that the scandium-zinc quasicrystal has high surface energy.

  This is important because in thermodynamics, energy is like cost. If you’re hungry and go to a department store, you buy the pack of biscuits that you can afford rather than wait until you have enough money to buy the most expensive one. Similarly, when there’s a hot mass of scandium-zinc as a liquid and scientists are slowly cooling it, the atoms will form the first solid phase they can access rather than wait until they have accumulated enough surface energy to access the quasicrystal phase. And the first phase they can access will be crystalline. On the other hand scientists discovered the ytterbium-cadmium quasicrystal so quickly because it has a modest amount of energy across its surface and thus when cooled from liquid to solid, the first solid phase the atoms can access is also the quasicrystal phase.

  This is an important discovery: the researchers found that a phase diagram alone can’t be used to say which phase will actually form. Understanding the surface-energy barrier is also important, and could pave the way to a practical roadmap for scientists trying to grow crystals for specific applications.

  The big question now is: what special bonding or electronic effects allow atoms to have order without periodicity? After Israeli scientist Dan Shechtman discovered quasicrystals in 1982, he didn’t publish his findings until two years later, after including some authors on his submission to improve its chances with a journal, because he thought he wouldn’t be taken seriously. This wasn’t a silly concern: Linus Pauling, one of the greatest chemists in the history of subject, dismissed Shechtman’s work and called him a “quasi-scientist”. The blowback was so sharp and swift because chemists like Pauling, who had helped establish the science of crystal structures, were certain there was a way crystals could look and a way they couldn’t — and quasicrystals didn’t have the right look. But now, the new study has found that quasicrystals look perfect. Perhaps it’s crystals that need to explain themselves…

  2025.06.26

• The Berry phase of Kancha Gachibowli

  There’s a concept in quantum mechanics, and also in parts of classical mechanics, called the Berry phase. Say you’re walking around a mountain. You start off along a path and follow it all the way until you’re back to the point where you started. You’re at the same point, sure, but you’re probably facing a different direction now. The Berry phase works something like this. Say you’ve got a bunch of electrons that you’re manipulating using a magnetic field. As you vary the field in continuous increments, the electrons will respond continuously in some way. But as you vary the field through a cycle of changes and bring it back to the original setting, the electrons won’t exactly be at their original configuration as well. Or they will be in addition to some change. This ‘additional change’ is called the Berry phase.

  Reading about the Kancha Gachibowli forest brought the Berry phase to mind. Yesterday, India’s new Chief Justice, B.R. Gavai, faced Telangana state with a choice: “between restoring the forest or having the Chief Secretary and [half a dozen] officials in prison,” per The Hindu. The latter people are being held responsible for attempting to divert mostly moderately and densely forested land to a planned campus for information technology companies. The court had no sympathy for Telangana counsel Abhishek Manu Singhvi’s argument that the state’s efforts had been good-intentioned. The principle reason: the state hasn’t been able to explain the fact that it organised a phalanx of bulldozers to bring down 104 acres of old trees during an extended weekend, when the courts were closed, leaving the felling’s opponents without access to legal recourse. A few telling passages from The Hindu:

  The State had previously denied the land was a forest. The claim, it said, that the area was forest land had sprung up only after developmental activities commenced following the allotment of the land to the Telangana Industrial Infrastructure Corporation. Mr. Singhvi submitted that the processes regarding the allotment had been on since March 2024. He said the intention of the State was bona fide.

  …

  Mr. Singhvi maintained that “thousands” of trees were not cut. “We have seen the photographs,” Chief Justice Gavai responded.

  Mr. Singhvi submitted that not a leaf has been moved on the site after the apex court ordered everything to be stopped on April 16. The State was complying with the court’s direction in letter and spirit. A huge afforestation programme was underway in the area.

  Amicus curiae, senior advocate K. Parameshwar, drew the attention of the court to a finding in a Forest Survey of India report, which was forwarded to the Central Empowered Committee, that out of the 104 acres cut in two nights, over 60% had been moderately and heavily dense forest.

  It’s worthwhile these days to treat the concept of afforestation as a yellow flag at best and a despicable idea at worst. In the last decade it has evolved regressively into a sort of olive branch offered up alongside casual excuses to divert forested land for non-forest uses, often in open defiance of India’s existing forest protection laws — which sadly have been increasingly enfeebled by the environment ministry. That the state is now afforesting the area is little consolation because the trees that have already been cut represent a greater ecological loss than that can be recouped by young plants anytime in the near future. We may have come full circle since the state first felled the trees but we bear the burden of an additional change as well.

  In fact, this could be more like magnetic hysteresis than the Berry phase depending on the mode of afforestation. Quantum systems are said to have acquired a Berry phase when they undergo a reversible process in which entropy doesn’t increase*. But entropy, the amount of disorder, has indeed increased. We’ve lost energy. We’ve lost old trees and their ecosystem services. We’ve lost a sustainable carbon store. We’ve learnt that the Telangana government is willing to act in bad faith. We’ve learnt that our forest protection laws continue to not work. Why, we’ve been reminded that the Supreme Court remains the country’s last democratic institution, perhaps short of Parliamentary majority, prepared to measure the loss of green cover by the precepts of sustainable development. Every Supreme Court decision to stall a project that entails deforestation has been met with cheers in the conservation and environmental justice communities but each such verdict also serves a reminder that we remain at the mercy of the last line of defence. If someday the Supreme Court also yields, or is let down by Parliament passing a law that makes a mockery of protecting trees, we are only left with protest — like the brave students of the University of Hyderabad mounted to bring the Kancha Gachibowli issue to the whole country’s attention.

  When you apply a magnetic field over a ferromagnet, like a block of iron, it becomes magnetised. If you remove the magnetic field, the block stays magnetised to some degree. This phenomenon is called remanence. Future attempts to magnetise and demagnetise the block will have to work against the remanence, causing the block to lose energy over time as heat. This macroscopic feature is called magnetic hysteresis**: it’s irreversible, dissipative, disorderly, and vexatious. Much like the state of Telangana, it claims to find value in the context of computers (disk drives in particular), and much like the trees of Kancha Gachibowli, there’s nothing a ferromagnet can do about it.

  ---

  * I’ve used entropy here with reference to a quantum adiabatic process. In a thermodynamic adiabatic process, entropy isn’t produced only if the process is also reversible.

  ** The term ‘hysteresis’ comes from the Greek ‘hústeros’, meaning ‘later’. This is a reference to the shape of the curve on a graph with the strength of the magnetic field H on one axis and the magnetisation M on the other. As the H curve rises and falls, the M curve starts to fall behind. The seemingly closely related ‘hysteria’ comes from the Greek ‘hustéra’, for ‘womb’, and is thus unrelated. However, the well-known Cornell University physicist James P. Sethna wrote sometime before 1995:

  There seems to be no etymological link between hysteresis and either hysterical (fr. L hystericus of the womb) or history (fr. Gk, inquiry, history, fr. histor, istor knowing, learned). This is too bad, as there are scientific connections to both words. (There is no link, scientific or etymological, to histolysis, the breakdown of bodily tissues, or to blood.) … Many hysteretic systems make screeching noises as they respond to their external load (hence, the natural connection with hysteria).

  ‘Hysteria’ has of course rightly fallen out of favour both within and without clinical contexts.

  2025.05.16

• The weekly linklist – July 25, 2020

  I’ve decided to publish this linklist via Substack. Next weekend onwards, it will only be available on https://linklist.substack.com. And this is why the list exists and what kind of articles you can find in it.

  • Want to buy a parrot? Please login via Facebook. – “F-commerce emerged in Bangladesh largely because there was no major e-commerce platform to absorb all the business. But although it’s biggest there, this form of selling isn’t exclusive to the country, or even the region: globally, 160 million small stores operate on Facebook, and in countries like Thailand, almost half of all online sales happen through social media.”
  • The history of climate science – “The fact that carbon dioxide is a ‘greenhouse gas’ – a gas that prevents a certain amount of heat radiation escaping back to space and thus maintains a generally warm climate on Earth, goes back to an idea that was first conceived, though not specifically with respect to CO2, nearly 200 years ago. The story of how this important physical property was discovered, how its role in the geological past was evaluated and how we came to understand that its increased concentration, via fossil fuel burning, would adversely affect our future, covers about two centuries of enquiry, discovery, innovation and problem-solving.”
  • The story of cryptomining in Europe’s most disputed state – “In early 2018, millions of digital clocks across Europe began falling behind time. Few took notice at first as slight disruptions in the power supply caused bedside alarms and oven timers running on the frequency of electric current to begin lagging. … European authorities soon traced the power fluctuations to North Kosovo, a region commonly described as one of Europe’s last ganglands. Since 2015, its major city, Mitrovica, has been under the control of Srpska Lista, a mafia masquerading as a political party. Around the time Srpska came to power, North Kosovo’s electricity consumption surged. Officials at the Kosovo Electricity Supply Company in Prishtina, Kosovo’s capital city, told me that the region now requires 20 percent more power than it did five years ago. Eventually, it became clear why: across the region, from the shabby apartment blocks of Mitrovica to the cellars of mountain villages, Bitcoin and Ethereum rigs were humming away, fueling a shadow economy of cryptocurrency manufacturing.”
  • Electromagnetic pulses are the last thing you need to worry about in a nuclear explosion – “The electromagnetic pulse that comes from the sundering of an atom, potentially destroying electronics within the blast radius with some impact miles away from ground zero, is just one of many effects of every nuclear blast. What is peculiar about these pulses, often referred to as EMPs, is the way the side effect of a nuclear blast is treated as a special threat in its own right by bodies such as the Task Force on National and Homeland Security, which, despite the official-sounding name, is a privately funded group. These groups continue a decadelong tradition of obsession over EMPs, one President Donald Trump and others have picked up on.”
  • India’s daunting challenge: There’s water everywhere, and nowhere – “I am walking across the world. Over the past seven years I have retraced the footsteps of Homo sapiens, who roamed out of Africa in the Stone Age and explored the primordial world. En route, I gather stories. And nowhere on my foot journey—not in any other nation or continent—have I encountered an environmental reckoning on the scale of India’s looming water crisis. It is almost too daunting to contemplate.”
  • Here be black holes – “During the 15th and 16th centuries, when oceans were the spaces between worlds, marine animals, often so prodigious that they were termed sea monsters, were difficult to see and even harder to analyse, their very existence uncertain. Broadly construed, the history of space science is also a story of looking across and into the ocean – that first great expanse of space rendered almost unknowable by an alien environment. Deep space, like the deep sea, is almost inaccessible, with the metaphorical depth of space echoing the literal depth of oceans. These cognitive and psychic parallels also have an analogue in the practicalities of survival, and training for space missions routinely includes stints under water.”
  • Birds bear the warnings but humans are responsible for the global threat – “Bird omens of a sort are the subject of two recent anthropological studies of avian flu preparedness in Asia. Both Natalie Porter, in Viral Economies, and Frédéric Keck, in Avian Reservoirs, convey the ominousness suffusing poultry farming, using birds as predictors. As both demonstrate, studying how birds interact with human agriculture can provide early warnings of a grim future. Indeed, Keck in Avian Reservoirs explicitly compares public-health surveillance (which he studies in the book) to augury, tracing ‘the idea that birds carry signs of the future that humans should learn to read … back to Roman divination.’”
  • Fiction as a window into the ethics of testing the Bomb – “The stuff that surprised me was on the American side. For example, the assessment by Curtis LeMay [the commander who led US air attacks on Japan] where he basically says, “We’ve bombed the shit out of Japan. Hurry up with your atomic bomb, because there’s going to be nothing left if you don’t.” That shocked me, and also that they deliberately left those cities pristine because they wanted to show the devastation. They wanted, I believe, to kill innocent people, because they were already moving on to the Cold War.”
  • The idea of entropy has led us astray – “Perhaps physics, in all its rigors, is deemed less susceptible to social involvement. In truth, though, Darwinian and thermodynamic theories served jointly to furnish a propitious worldview—a suitable ur-myth about the universe—for a society committed to laissez-faire competition, entrepreneurialism, and expanding industry. Essentially, under this view, the world slouches naturally toward a deathly cold state of disorder, but it can be salvaged—illuminated and organized—by the competitive scrabble of creatures fighting to survive and get ahead.”
  • How massive neutrinos broke the Standard Model – “Niels Bohr … had the radical suggestion that maybe energy and momentum weren’t really conserved; maybe they could somehow be lost. But Wolfgang Pauli had a different — arguably, even more radical — thought: that perhaps there was a novel type of particle being emitted in these decays, one that we simply didn’t yet have the capacity to see. He named it “neutrino,” which is Italian for “little neutral one,” and upon hypothesizing it, remarked upon the heresy he had committed: ‘I have done a terrible thing, I have postulated a particle that cannot be detected.’”
  • How a small Arab nation built a Mars mission from scratch in six years – “When the UAE announced in 2014 that it would send a mission to Mars by the country’s 50th birthday in December 2021, it looked like a bet with astronomically tough odds. At the time, the nation had no space agency and no planetary scientists, and had only recently launched its first satellite. The rapidly assembled team of engineers, with an average age of 27, frequently heard the same jibe. ‘You guys are a bunch of kids. How are you going to reach Mars?’ says Sarah Al Amiri, originally a computer engineer and the science lead for the project.”
  • The pandemic has made concentrated reading difficult. How are book reviewers dealing with this? – “To read good and proper, I needed to disconnect from the terrible reality of the present – wishful thinking with the always-on-alert mode that the pandemic thrust upon us. A few pages in, my mind would wander, snapping out of the brief, quiet moment and I’d find myself reaching for my phone. … But as neuroscientists world over have told us, it’s been hard for most people to focus, with our brain in fight-or-flight mode to the threat of the virus. An activity like deep reading is especially difficult because it requires a high level of engagement and quiet. So it wasn’t just me.”
  • Facebook’s employees reckon with the social network they’ve built – “Why was Zuckerberg only talking about whether Trump’s comments fit the company’s rules, and not about fixing policies that allowed for threats that could hurt people in the first place, he asked. ‘Watching this just felt like someone was sort of slowly swapping out the rug from under my feet,’ Wang said. ‘They were swapping concerns about morals or justice or norms with this concern about consistency and logic, as if it were obviously the case that ‘consistency’ is what mattered most.’”

  2020.07.25

• Journalistic entropy

  Say you need to store a square image 1,000 pixels wide to a side with the smallest filesize (setting aside compression techniques). The image begins with the colour #009900 on the left side and, as you move towards the right, gradually blends into #1e1e1e on the rightmost edge. Two simple storage methods come to mind: you could either encode the colour-information of every pixel in a file and store that file, or you could determine a mathematical function that, given the inputs #009900 and #1e1e1e, generates the image in question.

  The latter method seems more appealing, especially for larger canvases of patterns that are composed by a single underlying function. In such cases, it should obviously be more advantageous to store the image as an output of a function to achieve the smallest filesize.

  

  Now, in information theory (as in thermodynamics), there is an entity called entropy: it describes the amount of information you don’t have about a system. In our example, imagine that the colour #009900 blends to #1e1e1e from left to right save for a strip along the right edge, say, 50 pixels wide. Each pixel in this strip can assume a random colour. To store this image, you’d have to save it as an addition of two functions: ƒ(x, y), where x = #009900 and y = #1e1e1e, plus one function to colour the pixels lying in the 50-px strip on the right side. Obviously this will increase the filesize of the stored function.

  Even more, imagine if you were told that 200,000 pixels out of the 1,000,000 pixels in the image would assume random colours. The underlying function becomes even more clumsy: an addition of ƒ(x, y) and a function R that randomly selects 200,000 pixels and then randomly colours them. The outputs of this function R stands for the information about the image that you can’t have beforehand; the more such information you lack, the more entropy the image is said to have.

  The example of the image was simple but sufficiently illustrative. In thermodynamics, entropy is similar to randomness vis-à-vis information: it’s the amount of thermal energy a system contains that can’t be used to perform work. From the point of view of work, it’s useless thermal energy (including heat) – something that can’t contribute to moving a turbine blade, powering a motor or motivating a system of pulleys to lift weights. Instead, it is thermal energy motivated by and directed at other impetuses.

  As it happens, this picture could help clarify, or at least make more sense of, a contemporary situation in science journalism. Earlier this week, health journalist Priyanka Pulla discovered that the Indian Council of Medical Research (ICMR) had published a press release last month, about the serological testing kit the government had developed, with the wrong specificity and sensitivity data. Two individuals she spoke to, one from ICMR and another from the National Institute of Virology, Pune, which actually developed the kit, admitted the mistake when she contacted them. Until then, neither organisation had issued a clarification even though it was clear both individuals are likely to have known of the mistake at the time the release was published.

  Assuming for a moment that this mistake was an accident (my current epistemic state is ‘don’t know’), it would indicate ICMR has been inefficient in the performance of its duties, forcing journalists to respond to it in some way instead of focusing on other, more important matters.

  The reason I’m tending to think of such work as entropy and not work per se is such instances, whereby journalists are forced to respond to an event or action characterised by the existence of trivial resolutions, seem to be becoming more common.

  It’s of course easier to argue that what I consider trivial may be nontrivial to someone else, and that these events and actions matter to a greater extent than I’m willing to acknowledge. However, I’m personally unable to see beyond the fact that an organisation with the resources and, currently, the importance of ICMR shouldn’t have had a hard time proof-reading a press release that was going to land in the inboxes of hundreds of journalists. The consequences of the mistake are nontrivial but the solution is quite trivial.

  (There is another feature in some cases: of the absence of official backing or endorsement of any kind.)

  So as such, it required work on the part of journalists that could easily have been spared, allowing journalists to direct their efforts at more meaningful, more productive endeavours. Here are four more examples of such events/actions, wherein the non-triviality is significantly and characteristically lower than that attached to formal announcements, policies, reports, etc.:

  1. Withholding data in papers – In the most recent example, ICMR researchers published the results of a seroprevalence survey of 26,000 people in 65 districts around India, and concluded that the prevalence of the novel coronavirus was 0.73% in this population. However, in their paper, the researchers include neither a district-wise breakdown of the data nor the confidence intervals for each available data-point even though they had this information (it’s impossible to compute the results the researchers did without these details). As a result, it’s hard for journalists to determine how reliable the results are, and whether they really support the official policies regarding epidemic-control interventions that will soon follow.
  2. Publishing faff – On June 2, two senior members of the Directorate General of Health services, within India’s Union health ministry, published a paper (in a journal they edited) that, by all counts, made nonsensical claims about India’s COVID-19 epidemic becoming “extinguished” sometime in September 2020. Either the pair of authors wasn’t aware of their collective irresponsibility or they intended to refocus (putting it benevolently) the attention of various people towards their work, turning them away from the duo deemed embarrassing or whatever. And either way, the claims in the paper wound their way into two news syndication services, PTI and IANS, and eventually onto the pages of a dozen widely-read news publications in the country. In effect, there were two levels of irresponsibility at play: one as embodied by the paper and the other, by the syndication services’ and final publishers’ lack of due diligence.
  3. Making BS announcements – This one is fairly common: a minister or senior party official will say something silly, such as that ancient Indians invented the internet, and ride the waves of polarising debate, rapidly devolving into acrimonious flamewars on Twitter, that follow. I recently read (in The Washington Post I think, but I can’t find the link now) that it might be worthwhile for journalists to try and spend less time on fact-checking a claim than it took someone to come up with that claim. Obviously there’s no easy way to measure the time some claims took to mature into their present forms, but even so, I’m sure most journalists would agree that fact-checking often takes much longer than bullshitting (and then broadcasting). But what makes this enterprise even more grating is that it is orders of magnitude easier to not spew bullshit in the first place.
  4. Conspiracy theories – This is the most frustrating example of the lot because, today, many of the originators of conspiracy theories are television journalists, especially those backed by government support or vice versa. While fully acknowledging the deep-seated issues underlying both media independence and the politics-business-media nexus, numerous pronouncements by so many news anchors have only been akin to shooting ourselves in the foot. Exhibit A: shortly after Prime Minister Narendra Modi announced the start of demonetisation, a beaming news anchor told her viewers that the new 2,000-rupee notes would be embedded with chips to transmit the notes’ location real-time, via satellite, to operators in Delhi.

  Perhaps this entropy – i.e. the amount of journalistic work not available to deal with more important stories – is not only the result of a mischievous actor attempting to keep journalists, and the people who read those journalists, distracted but is also assisted by the manifestation of a whole industry’s inability to cope with the mechanisms of a new political order.

  Science journalism itself has already experienced a symptom of this change when pseudoscientific ideas became more mainstream, even entering the discourse of conservative political groups, including that of the BJP. In a previous era, if a minister said something, a reporter was to drum up a short piece whose entire purpose was to record “this happened”. And such reports were the norm and in fact one of the purported roots of many journalistic establishments’ claims to objectivity, an attribute they found not just desirable but entirely virtuous: those who couldn’t be objective were derided as sub-par.

  However, if a reporter were to simply report today that a minister said something, she places herself at risk of amplifying bullshit to a large audience if what the minister said was “bullshit bullshit bullshit”. So just as politicians’ willingness to indulge in populism and majoritarianism to the detriment of society and its people has changed, so also must science journalism change – as it already has with many publications, especially in the west – to ensure each news report fact-checks a claim it contains, especially if it is pseudoscientific.

  In the same vein, it’s not hard to imagine that journalists are often forced to scatter by the compulsions of an older way of doing journalism, and that they should regroup on the foundations of a new agreement that lets them ignore some events so that they can better dedicate themselves to the coverage of others.

  Featured image credit: Татьяна Чернышова/Pexels.

  2020.06.14

• Time and the pandemic

  There is this idea in physics that the fundamental laws of nature apply the same way for processes moving both forwards and backwards in time. So you can’t actually measure the passage of time by studying these processes. Where does our sense of time, rather the passage of time, come from then? How do we get to tell that the past and future are two different things, and that time flows from the former to the latter?

  We sense time because things change. Clock time is commonly understood to be a way to keep track of when and how often things change but in physics, time is not the master: change doesn’t arise because of time but time arises because of change. So time manifests in the laws of nature through things that change in time. One of the simplest such things is entropy. Specifically, the second law of thermodynamics states that as time moves forward, the entropy of an isolated system cannot decrease. Entropy thus describes an arrow of time.

  This is precisely what the pandemic is refusing to do, at least as seen through windows set at the very back of a newsroom. Many reporters writing about the coronavirus may have the luxury of discovering change, and therefore the forward march of time itself, but for someone who is somewhat zoomed out – watching the proceedings from a distance, as it were – the pandemic has only suffused the news cycle with more and more copies of itself, like the causative virus itself.

  It seems to me as if time has stilled. I have become numb to news about the virus, which I suspect is a coping mechanism, like a layer of armour inserted between a world relentlessly pelting me with bad news and my psyche itself. But the flip side of this protection is an inability to sense the passage of time as well as I was able before.

  My senses are alert to mistakes of fact, as well as mostly of argument, that reporters make when reporting on the coronavirus, and of course to opportunities to improve sentence construction, structure, flow, etc. But otherwise, and thanks in fact to my limited engagement with this topic, it feels as if I wake up every morning, my fingers groaning at the prospect of typing the words “lockdown”, “coronavirus”, “COVID-19”, “herd immunity” and whatever else¹. And since this is what I feel every morning, there is no sense of change. And without change, there is no time.

  1. I mean no offence to those suffering the pandemic’s, and the lockdown’s, brutal health, economic, social, cultural and political consequences.

  I would desperately like to lose my armour. The bad news will never stop coming but I would still like to get back to bad news that I got into journalism to cover, the bad news that I know what to do about… to how things were before, I suppose.

  Oh, I’m aware of how illogical this line of introspection is, yet it persists! I believe one reason is that the pandemic is a passing cloud. It leapt out of the horizon and loomed suddenly over all of us, over the whole world; its pall is bleak but none of us doubts that it will also pass. The pandemic will end – everybody knows this, and this is perhaps also why the growing desperation for it to dissipate doesn’t feel misplaced, or unjustified. It is a cloud, and like all clouds, it must go away, and therefrom arises the frustration as well: if it can go away, why won’t it?

  Is it true that everything that will last for a long time also build up over a long time? Climate change, for example, doesn’t – almost can’t – have a single onset event. It builds and builds all around us, its effects creeping up on us. With each passing day of inaction, there is even less that we can do than before to stop it; in fact, so many opportunities have been squandered or stolen by bad actors that all we have left to do is reduce consumption and lower carbon emissions. So with each passing day, the planet visits us with more reminders of how we have changed it, and in fact may never have it back to the way it once was.

  Almost as if climate change happened so slowly, on the human scale at least, that it managed to weave itself into our sense of time, not casting a shadow on the clock as much as becoming a part of the clock itself. As humankind’s grandest challenge as yet, one that we may never fully surmount, climate change doesn’t arise because of time but time arises because of climate change. Perhaps speed and surprise is the sacrifice that time demands of that which aspires to longevity.

  The pandemic, on the other hand, likely had a single onset… right? At least it seems so until you realise the pandemic is in fact the tip of the proverbial iceberg – the thing jutting above the waterline, better yet the tip of the volcano. There is a complicated mess brewing underground, and out of sight, to which we have all contributed. One day the volcano shoots up, plastering its surroundings with lava and shooting smoke and soot kilometres into the air. For a time, the skies are a nuclear-winter grey and the Sun is blotted out. To consider at this time that we could stave off all future eruptions by pouring tonnes of concrete into the smouldering caldera would be folly. The pandemic, like magma, like the truth itself, will out. So while the nimbuses of each pandemic may pass, all the storm’s ingredients will persist.

  I really hope the world, and I do mean the world, will heed this lesson as the novel coronavirus’s most important, if only because our sense of time and our expectations of what the passage of time could bring need to encompass the things that cause pandemics as much as they have come to encompass the things that cause Earth’s climate to change. We’ve become used to thinking about this outbreak, and likely the ones before it, as transitory events that begin and end – but really, wrapped up in our unrelenting yearning for the pandemic to pass is a conviction that the virus is a short-lived, sublunary creature. But the virus is eternal, and so our response to it must also transform from the mortal to the immortal.

  Then again, how I wish my mind submitted, that too just this once, to logic’s will sans resistance. No; it yearns still for the pandemic to end and for ‘normal’ to recommence, for time to flow as it once did, with the promise of bringing something new to the threshold of my consciousness every morning. I sense there is a line here between the long- and the short-term, between the individual and the collective, and ultimately between the decision to change myself and the decision to wait for others before I do.

  I think, as usual, time will tell. Heh.

  2020.04.19

• A journey through Twitter and time, with the laws of physics

  Say you’re in a dark room and there’s a flash. The light travels outward in all directions from the source, and the illumination seems to expand in a sphere. This is a visualisation of how the information contained in light becomes distributed through space.

  But even though this is probably what you’d see if you observed the flash with a very high speed camera, it’s not the full picture. The geometry of the sphere captures only the spatial component of the light’s journey. It doesn’t say anything about the time. We can infer that from how fast the sphere expands but that’s not an intrinsic property of the sphere itself.

  To solve this problem, let’s assume that we live in a world with two spatial dimensions instead of three (i.e. length and breadth only, no depth). When the flash goes off in this world, the light travels outward in an expanding circle, which is the two-dimensional counterpart of a sphere. At 1 second after the flash, say the circle is 2 cm wide. After 2 seconds, it’s 4 cm wide. After 3 seconds, it’s 8 cm wide. After 4 seconds, it’s 16 cm wide. And so forth.

  If you photographed the circles at each of these moments and put the pictures together, you’d see something like this (not to scale):

  

  And if you looked at this stack of circles from under/behind, you’d see what physicists call the light cone.

  

  The cone is nothing but a stack of circles of increasing diameter. The circumference of each circle represents the extent to which the light has spread out in space at that time. So the farther into the future of an event – such as the flash – you go, the wider the light cone will be.

  (The reason we assumed we live in a world of two dimensions instead of three should be clearer now. In our three-dimensional reality, the light cone would assume a four-dimensional shape that can be quite difficult to visualise.)

  According to the special theory of relativity, all future light cones must be associated with corresponding past light cones, and light always flows from the past to the future.

  To understand what this means, it’s important to understand the cones as exclusionary zones. The diameter of the cone at a specific time is the distance across which light has moved in that time. So anything that moves slower – such as a message written on a piece of paper tied to a rock thrown from A to B – will be associated with a narrower cone between A and B. If A and B are so far apart that even light couldn’t have spanned them in the given time, then B is going to be outside the cone emerging from A, in a region officially called elsewhere.

  Now, light is just one way to encode information. But since nothing can move faster than at the speed of light, the cones in the diagram above work for all kinds of information, i.e. any other medium will simply be associated with narrower cones but the general principles as depicted in the diagram will hold.

  For example, here’s something that happened on Twitter earlier today. I spotted the following tweet at 9.15 am:

  Whaaat??? Professor not valid for what gender???
  @airvistara a little behind times are we not???
  Professor Shyama Rath @rath_shyama is a Professor of Physics, Delhi University and female!!
  Please change your inherent biases now!! https://t.co/uCQmxZCk5H

  — Shailja Vaidya Gupta (@himdaughter) July 25, 2019

  When scrolling through the replies, I noticed that one of Air Vistara’s senior employees had responded to the complaint with an apology and an assurance that it would be fixed.

  https://twitter.com/TheSanjivKapoor/status/1154223981358018561

  Taking this to be an admission of guilt, and to an admission of there actually having been a mistake by proxy, I retweeted the tweet at 9.16 am. However, only a minute later, another account discovered that the label of ‘professor’ didn’t work with the ‘male’ option either, ergo the glitch didn’t have so much to do with the user’s gender as much as the algorithm was just broken. A different account brought this to my attention at 9.30 am.

  So here we have two cones of information that can be recast as the cones of causality, intersecting at @rath_shyama’s tweet. The first cone of causality is the set of all events in the tweet’s past whose information contributed to it. The second cone of causality represents all events in whose past the tweet lies, such as @himdaughter’s, the other accounts’ and my tweets.

  As it happens, Twitter interferes with this image of causality in a peculiar way (Facebook does, too, but not as conspicuously). @rath_shyama published her tweet at 8.02 am, @himdaughter quote-tweeted her at 8.16 am and I retweeted @himdaughter at 9.16 am. But by 9.30 am, the information cone had expanded enough for me to know that my retweet was possibly mistaken. Let’s designate this last bit of information M.

  So if I had un-retweeted @himdaughter’s tweet at, say, 9.31 am, I would effectively have removed an event from the timeline that actually occurred before I could have had the information to act on it (i.e., M). The issue is that Twitter doesn’t record (at least not publicly anyway) the time at which people un-retweet tweets. If it had, then there would have been proof that I acted in the future of M; but since it doesn’t, it will look like I acted in the past of M. Since this is causally impossible, the presumption arises that I had the information about M before others did, which is false.

  This serves as an interesting commentary on the nature of history. It is not possible for Twitter’s users to remember historical events on its platform in the right order simply because Twitter is memoryless when it comes to one of the actions it allows. As a journalist, therefore, there is a bit of comfort in thinking about the pre-Twitter era, when all newsworthy events were properly timestamped and archived by the newspapers of record.

  However, I can’t let my mind wander too far back, lest I stagger into the birth of the universe, when all that existed was a bunch of particles.

  

  We commonly perceive that time has moved forward because we also observe useful energy becoming useless energy. If nothing aged, if nothing grew weaker or deteriorated in material quality – if there was no wear-and-tear – we should be able to throw away our calendars and pretend all seven days of the week are the same day, repeated over and over.⁺

  Scientists capture this relationship between time and disorderliness in the second law of thermodynamics. This law states that the entropy – the amount of energy that can’t be used to perform work – of a closed system can never decrease. It can either remain stagnant or increase. So time does not exist as an entity in and of itself but only seems to as a measure of the increase in entropy (at a given temperature). We say a system has moved away from a point in its past and towards a point in its future if its entropy has gone up.

  However, while this works just fine with macroscopic stuff like matter, things are a bit different with matter’s smallest constituents: the particles. There are no processes in this realm of the quantum whose passage will tell you which way time has passed – at least, there aren’t supposed to be.

  There’s a type of particle called the B⁰ meson. In an experiment whose results were announced in 2012, physicists found unequivocal proof that this particle transformed into another one faster than the inverse process. This discrepancy provides an observer with a way to tell which way time is moving.

  The experiment also remains the only occasion till date on which scientists have been able to show that the laws of physics don’t apply the same forward and backward in time. If they did, the forward and backward transformations would have happened at the same rate, and an observer wouldn’t have been able to tell if she was watching the system move into the future or into the past.

  But with Twitter, it would seem we’re all clearly aware that we’re moving – inexorably, inevitably – into the future… or is that the past? I don’t know.

  ⁺ And if capitalism didn’t exist: in capitalist economies, inequality always seems to increase with time.

  2019.07.27

• Why a pump to move molten metal is awesome

  The conversion of one form of energy into another is more efficient at higher temperatures.¹ For example, one of the most widely used components of any system that involves the transfer of heat from one part of the system to another is a device called a heat exchanger. When it’s transferring heat from one fluid to another, for example, the heat exchanger must facilitate the efficient movement of heat between the two media without allowing them to mix.

  There are many designs of heat exchangers for a variety of applications but the basic principle is the same. However, they’re all limited by the explicit condition that entropy – “the measure of disorder” – is higher at lower temperatures. In other words, the lower the temperature difference within the exchanger, the less efficiently the transfer will happen. This is why it’s desirable to have a medium that can carry a lot of heat per unit volume.

  But this is not always possible for two reasons. First: there must exist a pump that can move such a hot medium from one point to another in the system. This pump must be made of materials that can withstand high temperatures during operation as well as not react with the medium at those temperatures. Second: one of the more efficient media that can carry a lot of heat is liquid metals. But they’re difficult to pump because of their corrosive nature and high density. Both reasons together, this is why medium temperatures have been limited to around 1,000º C.

  Now, an invention by engineers from the US has proposed a solution. They’ve constructed a pump using ceramics. This is really interesting because ceramics have a good reputation for being able to withstand extreme heat (they were part of the US Space Shuttle’s heat shield exposed during atmospheric reentry) but an equally bad reputation for being very brittle.² So this means that a ceramic composition of the pump material accords it a natural ability to withstand heat.

  In other words, the bigger problem the engineers would’ve solved for would be to keep it from breaking during operation.

  Their system consists of a motor, a gearbox, pipes and a reservoir of liquid tin. When the motor is turned on, the pump receives liquid tin from the bottom of the reservoir. Two interlocking gears inside the pump rotate. As the tin flows between the blades, it is compressed into the space between them, creating a pressure difference that sucks in more tin from the reservoir. After the tin moves through the blades, it is let out into another pipe that takes it back to the reservoir.

  The blades are made of Shapal, an aluminium nitride ceramic made by the Tokuyama Corporation in Japan with the unique property of being machinable. The pump seals and the pipes are made of graphite. High-temperature pumps usually have pipes made of polymers. Graphite and such polymers are similar in that they’re both very difficult to corrode. But graphite has an upper hand in this context because it can also withstand higher temperatures before it loses its consistency.

  Using this setup, the engineers were able to operate the pump continuously for 72 hours at an average temperature of 1,200º C. For the first 60 hours of operation, the flow rate varied between 28 and 108 grams per second (at an rpm in the lower hundreds). According to the engineers’ paper, this corresponds to an energy transfer of 5-20 kW for a vat of liquid tin heated from 300º C to 1,200º C. They extrapolate these numbers to suggest that if the gear diameter and thickness were enlarged from 3.8 cm to 17.1 cm and 1.3 cm to 5.85 cm (resp.) and operated at 1,800 rpm, the resulting heat transfer rate would be 100 MW – a jump of 5,000x from 20 kW and close to the requirements of a utility-scale power plant.

  And all of this would be on a tabletop setup. This is the kind of difference having a medium with a high energy density makes.

  The engineers say that their choice of temperature at which to run the pump – about 1,200ºC – was limited by whatever heaters they had available in their lab. So future versions of this pump could run for cheaper and at higher temperatures by using, say, molten silicon and higher grade ceramics than Shapal. Such improvements could have an outsize effect in our world because of the energy capacity and transfer improvements they stand to bring to renewable energy storage.

  1. I can attest from personal experience that learning the principles of thermodynamics is easier through application than theory – an idea that my college professors utterly failed to grasp.

  2. The ceramics used to pave the floor of your house and the ceramics used to pad the underbelly of the Space Shuttle are very different. For one, the latter had a foamy internal structure and wasn’t brittle. They were designed and manufactured this way because the ceramics of the Space Shuttle wouldn’t just have to withstand high heat – they would also have to be able to withstand the sudden temperature change as the shuttle dived from the -270º C of space into the 1,500º C of hypersonic shock.

  Featured image credit: Erdenebayar/pixabay.

  2017.12.12