thermal equilibrium

A thin film of neodymium nickelate, fifteen nanometers thick, sits on a neodymium gallate substrate. Below one hundred eighty kelvin it behaves as an insulator: electrons are locked inside their atomic cells and cannot move freely.

A translator who has memorized all the lines in advance responds instantly — no need to listen to the whole conversation again. That's how the new model works: instead of running atoms through a computer for hours, it immediately outputs the crystal's free energy at any temperature and pressure.

Inside an ultracold chamber, two atomic clouds collide: a few dozen cesium atoms acting as the working fluid, and thousands of rubidium atoms serving as the heat reservoir.

Hot water sometimes freezes faster than warm water: this odd fact is known as the Mpemba effect. Now something similar has been found in the quantum world: a state with weak entanglement (a special quantum connection between particles) can beat a more entangled one to the finish line.

It all started with stretching. In the first fractions of a second, the universe ballooned — physicists call this inflation. Then the rapid expansion gave way to a phase where the field's energy converted into ordinary particles.

The wind carries pollen, and each grain moves as if on its own. But once the air swirls into a vortex, the pollen trajectories can no longer be separated: they are tangled. This is roughly how electrons behave in a strange metal: their motion is so strongly coupled to soft fluctuations of the medium that the usual particle carriers disappear.

A cup of hot coffee sometimes freezes faster than cold tap water. This paradox, known as the Mpemba effect, has long been considered a curiosity of classical physics. Now its quantum counterpart has helped test and tune quantum processors — devices that may one day power supercomputers.

Hot water sometimes freezes faster than cold. Ice forms more quickly from boiling water. This paradox, discovered by schoolboy Erasto Mpemba, long puzzled physicists. It turns out: the farther a system is from equilibrium, the faster it relaxes back to it. The Mpemba effect remains controversial today: too many variables, hard to reproduce.

A runner trails the leader but crosses the finish line first. In the quantum world, such a trick was pulled off by a system of nuclear spins — tiny magnetic arrows of carbon-13 atoms in a diamond. This is a manifestation of the Mpemba effect: a state initially farther from equilibrium settles down faster than one closer to rest.

The Mpemba effect is a mystery where hot вода sometimes freezes faster than warm water. Usually this is attributed to how вода loses heat and энтропию (a measure of disorder). But in a glass of water, chaos prevents a precise model. Physicists built a quantum model: a particle in a well with two depressions separated by a barrier.

At the centers of many galaxies lurk supermassive black holes. One of them, Sagittarius A* at the heart of the Milky Way, has become a testing ground for a new idea. The authors of the work took Einsteinian gravity and added an unusual electromagnetic field to it.

The classical Mpemba paradox — hot water freezes faster than cold — has teased scientists for centuries. Only recently has nonequilibrium statistical mechanics explained it: it’s all about boundary conditions; the system seems to seek an excuse to “hit the wall” and speed up cooling.

Quantum tunneling — the ability of particles to pass through barriers forbidden by classical physics — powers stars with thermonuclear fusion, ignites primordial nucleosynthesis, and gives us flash memory.

A sugar cube dropped into tea dissolves, and soon the entire liquid is uniformly sweet. This path to equilibrium is so familiar that it seems obvious.

The old question of Maxwell’s demon, can an intelligent being circumvent the second law of thermodynamics and pump heat from cold to hot, gains new resonance in the quantum world.

In a hot mug, water sometimes freezes faster than in a warm one. This paradox is over half a century old and is called the Mpemba effect. It is usually attributed to fluid motion or evaporation. Now physicists have shown that a similar trick is possible without water, just through radiation of heat.

In boiling water you can see a prototype of a quantum trick: if part of the liquid turns into long-lived vapor bubbles, the main mass cools down. This is exactly what happens when you sharply jolt a system of interacting electrons: doublons flare up — pairs of particles that absorb excess energy and don’t decay for an astonishingly long time.

A glass of hot tea sometimes cools faster than a glass of warm tea. This paradox, known as the Mpemba effect, was long considered a curiosity from the world of liquids. But physicists have found it where no one expected: in the faint glow of organic films placed in a magnetic field.

The focus is on a black hole, but not an ordinary one. It carries a magnetic monopole and is surrounded by a dilaton — a field that blurs the familiar boundaries of space. The authors tested how stable such a system is to thermal jolts. A magnetic monopole is a hypothetical particle with a single magnetic pole.

A black hole is not just a cosmic vacuum cleaner. It is a region with such strong gravity that even light cannot escape it. But place it in a perfect fluid of dark matter and add a cloud of strings, thin filaments stretched across all of space, and the picture gets more complicated.

Hot water sometimes freezes before cold: this is the Mpemba effect. In the quantum realm, a similar paradox appears: the more the equilibrium is disrupted, the faster it recovers. It's like fleeing from disorder (entropy) in reverse: the system rushes toward order, and a large initial imbalance only helps.

When a massive star runs out of fuel, its core collapses under its own weight. A black hole forms — a region where gravity is so strong that even light can't escape. For a long time, it was thought that a point of infinite density, a singularity, lurks at the very center.

In a pot of soup, every grain is a tiny magnet that wants to flip opposite to its neighbor. Heat the soup, and the magnets start jittering, obeying the heat. But how do you know how unruly they are at each temperature? For an ordinary material, you'd calculate this on powerful computers by enumerating possibilities.

Hot tea in a freezer doesn't freeze all at once. First, tiny ice needles dart around — forming and melting until the temperature drops enough for the ice to set solid. The early universe behaved similarly as it cooled and changed its internal structure.

Ordinary water freezes as expected. But sometimes hot water turns to ice faster than cold — the Mpemba effect. Recently, a similar rule-breaking was found in quantum entanglement — the invisible link between particles discovered by Erwin Schrödinger.

If you stick two identical thermometers into a pot of hot water, they'll both read the same, and we relax, thinking the temperature is measured correctly. But in a rarefied gas heated to millions of degrees, this trick stops working.

In a pot of boiling soup, tiny droplets of fat occasionally flare up — a hundred times hotter than the broth. That's roughly how future fusion plasma works: the bulk of ions heats to hundreds of millions of degrees, while a small admixture of "fast" particles (born from nuclear fusion) is accelerated even further.

A pot of soup forgotten on the stove cools to room temperature. It seems everything has come to rest. But if you look inside with a quantum magnifying glass, you'll find that water molecules haven't frozen: they continue their dance. It's just that now the dance is steady, not turbulent like when boiling.

Since time immemorial, physicists have dreamed of tunnels piercing the cosmos — wormholes, capable of connecting far-flung corners of the Universe in an instant.

A pot of water on the stove eventually settles down: the temperature evens out, the liquid stops boiling. Physicists call this thermal equilibrium — a state where energy is distributed in the most probable way.

On the surface of a tiny sphere live two invisible fields, like two kinds of ripples on a soap bubble. These fields don't just oscillate on their own: they constantly influence each other, like musicians playing in unison. In a new study, physicists derived exact equations that describe how this ripple changes over time, heats up, and descends into chaos.

Hundreds of people on a dance floor stand at equal distances from each other — strict order, like in a crystal lattice. Slow music is thermal vibrations, making dancers sway slightly. If the music gets louder and faster, order collapses: everyone mixes. That's how thermal motion destroys ordered states of electrons in solids.

Hot tea cools down, and its temperature is the same throughout the cup. But in many systems (for example, in the rarefied gas between stars or in plasma) temperature is not uniform: in one place particles are faster, in another slower. Physicists call such systems "superstatistical": it's as if the tea consisted of many small regions, each with its own temperature.

Picture a packed bus where every passenger is an electron. In a superconductor, passengers pair up and move in sync, losing no energy. But in high-temperature superconductors like cuprates, this idyll only works when extra passengers are added. If you drop some off, the pairs start acting strangely.

An aluminum pot on the stove melts at 660 degrees Celsius — everyone knows that. But what happens if you heat aluminum a hundred times hotter? The liquid starts to boil, and here's the puzzle: at what exact temperature does that happen?

Water can be ice, liquid, or steam. Physicists call these states phases. In theory, each phase has its own measure — a way to describe how likely it is. But not every measure you can imagine occurs in nature. Some phases are real, while others are just mathematical illusions. Scientists have found a simple criterion that separates reality from mirage.

Superconductivity is when electric current flows without losses, like water through a perfectly smooth pipe. It usually occurs at very low temperatures, but there are materials where it appears at higher ones.

A doughnut-shaped magnetic trap holds plasma made of boron and hydrogen. Inside, the temperature rises above one hundred million degrees — hotter than the center of the Sun. At such heat, nuclei collide and fuse, releasing energy.

The Mpemba effect is surprising: hot water sometimes freezes faster than cold. Scientists built a simple model: a bead in a thick, honey-like medium, on a landscape with two dips and a wall at the edge. The bead moves viscously, unable to hop over the central bump.

Light and atoms, like dancers, can move in sync or out of step. When their interaction is anisotropic (that is, direction-dependent) the dance gets trickier. In a new study, physicists considered a model where many atoms (qubits) collectively interact with an anisotropic light field, and each component is connected to a thermal reservoir.