fluctuation-dissipation theorem

A laser beam passes through a glass cell filled with cesium vapor. The atoms in the vapor dart around chaotically, like a crowd at a train station: each one enters the beam, spends a moment there, and flies back out. Their internal state, something like the orientation of a tiny magnet, changes under the influence of light. If all atoms were identical and stationary, the signal would be steady.

A superfluid gas is like a crowd of people marching in step: each atom knows where to go and doesn't fall out of the common rhythm. But this crowd has three 'valleys'—three different directions it can take. In a new experiment, physicists made one valley slightly more 'favorable' than the others and watched how the crowd darted between them.

A courtroom interpreter is distracted by every rustle: the creak of a chair, a cough in the back row, the rustle of papers. By the end of the day, they are translating not what the witness said, but what they heard through the noise. Rare translation errors are not the result of a single loud shout, but of the accumulation of many small disturbances.

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 early Universe was like a tightly coiled spring. In the first moments, it expanded at an unimaginable rate — a phase called inflation. Usually, this is attributed to a special field, but there's another idea: spacetime itself twists like a spring, and this twisting (in physics, torsion) becomes the engine of expansion.

At the dawn of time, the universe experienced a brief moment of frantic expansion — inflation. Tiny quantum jitters of spacetime stretched to cosmic scales. These jitters, primordial fluctuations, became the seeds from which galaxies and stars later grew.

Glass lenses and mirrors appear perfectly smooth and still. But beneath the surface, a hidden life teems. Atoms in an amorphous material (a substance without a crystalline lattice) are packed haphazardly, and this disorder creates a complex energy landscape, like a mountainous region with countless hills and valleys.

When a particle carries a large amount of internal energy, like a massive spinning top, its motion can be split into a fast part and a slow part. The fast part is a jitter that barely affects the big picture. Physicists have developed a method to discard this jitter and keep only the slow, meaningful motion. It's like skimming the foam off boiling soup to see the clear broth underneath.

Inside a supercomputer, fifteen stable wave clumps — solitons — collide to form a halo of dark matter. These waves obey an equation that Erwin Schrödinger derived for electrons at the beginning of the 20th century, but now they paint a portrait of a giant galactic cocoon.

A molecule works like a marketplace: electron shoppers enter through two gates (contacts) and head for stalls with the most attractive goods — the chemically active spots. Previously, current was thought to spread evenly, but it turns out up to 90% of all flow rushes through these 'hot spots'. Reactive centers become superconducting highways inside the molecule.

A thin film of a special crystal (for instance, molybdenum disulfide) sits on a microscope stage. The temperature is just above the point where the material becomes a superconductor.

Machine learning has long ceased to be just a tool — it is becoming an investigator, independently fishing out the laws of nature from data. But how does a silicon mind come to understand?

In the brain's white matter, the signal travels along axons — long neuronal processes wrapped in an insulating myelin sheath. Water fills the space inside axons and outside, in the narrow gaps between fibers.

An orchestra of billions of cesium atoms struck a single note, and it sounded for 17 hours without fading. That’s no exaggeration: Chinese physicists created a continuous time crystal with a record-breaking lifespan. A time crystal is a system that breaks time symmetry, spontaneously pulsating in an unchanging rhythm.

Membraneless organelles, tiny factories inside the cell, defy conventional rules. Take the nucleolus: here ribosomal RNA is synthesized — long chains woven from carbon sugars, rich in oxygen phosphate groups, and stitched with hydrogen bonds, suspended in the watery environment of the nucleus.

Quantum matter rarely treats us to the spectacle of self-motion. Where the classical world teems with starling murmurations, fish schools, and bustling bacteria, quantum thermodynamics long remained serene.

Spintronics promises to transmit information not by charge but by spin, ridding microelectronics of its main enemy — Joule heating.

Imagine: superfluid helium-3 in a thin film receives a sudden heat shock. In that instant, a whole orchestra of collective oscillations awakens within it — like striking an invisible drum produces a multi-voiced chord. The Kibble–Zurek mechanism, familiar from the cracking of ice during rapid freezing, here acquires a quantum elegance.

Two-dimensional worlds never cease to amaze: here even crystal melting is not a symmetry breaking but a vortex drama discovered by Kosterlitz and Thouless. At the heart of this theater are topological сингулярности, whose energy and энтропия bargain for order. This language is common to сверхтекучести и сверхпроводимости.

A supersolid is matter that is both crystalline and fluid. It is created from atoms cooled almost to absolute zero. In new work, physicists obtained such a substance as a triangular lattice of droplets. Each droplet oscillates in its own rhythm.

Gravitational waves are not vibrations of matter, but tremors of spacetime itself, predicted by Albert Einstein. They travel at the speed of light and pass through objects, stretching and squeezing them.

The shape of a riverbed precisely follows the equation describing the growth of a universe with negative curvature. In the lab, water flowing over sand spontaneously carves a cross-section that matches the solution for the Anti-de Sitter model. A river tends toward a shape that maximizes bottom friction.

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.

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.

A laser strikes the crystal, and it responds with flashes of light, like a bell ringing after a blow. But if the bell is warm, its sound wavers and fades. Same here: the crystal's atoms constantly jitter from heat, and this jitter disrupts the electrons' smooth flight, making the light dim and blurry.

An ultracold cloud of atoms trapped in laser light can 'breathe': it rhythmically contracts and expands, much like lungs. Physicists have long been able to observe this breathing, but only now have they realized that its amplitude is not just a pretty picture: it is a precise measure of hidden energy jitters inside the cloud.

A neuron perceives electrical signals like an ultrasensitive microphone picking up the faintest vibrations.

A semiconductor film one atom thick is like a tightly stretched membrane. Light makes it flash: luminous points (excitons) are born, which quickly fade. Where the membrane is torn or crumpled, the glow flickers and stutters, like a string with a knot sounding off-key.

The assembly of a virus shell is like fastening a button: protein blocks must interlock in the correct order, and thermal fluctuations act like trembling fingers. With weak binding, the trembling helps find the right position — the shell closes faster.

In two neighboring ponds, the same microorganisms swim. Food appears now in one, now in the other — randomly, with no rule. After a month, there are a hundred times more of them in the first pond than in the second. No one chose where to live. Just luck. This is how disequilibrium works. While the environment keeps changing, abundances don't have time to even out.

Every few years, the warm current off the coast of Peru shifts, and fishermen come home empty-handed. This is El Niño, the breath of the tropical Pacific, which affects weather from Indonesia to California. Predicting its arrival is as hard as predicting where a stone thrown into a raging river will roll.

When a proton slams into a lead nucleus at the Large Hadron Collider, a swarm of particles is born. They fly off in all directions, but not entirely randomly: their motion resembles ripples on water from a thrown stone.

Bacteria in a drop of water jostle and swim: each on its own, but together they create patterns. With weak motion, the fluid churns like soup on a high flame: vortices collide, and the flow direction changes every second. This is called bacterial turbulence.

When water churns behind a boat, the energy of motion is converted into heat through a cascade of vortices. Measuring how quickly this happens directly is difficult: you'd need to track all the vortices at once. So scientists use a simplification: they look at only one velocity component at a single point.

Every machine, whether a car engine or a tiny nanocooler, runs with a jitter. Fuel burns unevenly, electrons slip through contacts off schedule, and the power needle on your instruments vibrates slightly. These vibrations are called fluctuations. They are not just noise: they tell you how stable a device is and how much energy it wastes.

Water in a glass settles down once you stop stirring it. Oil in an engine dampens vibrations. It seems viscosity is always about damping. But in some flows, it's the opposite: add friction, and waves start to grow as if from nowhere. Physicists have found a simple explanation.

In the TiSe2 crystal, electrons behave like compass needles that suddenly start pointing in the same direction. This is called a nematic state — by analogy with liquid crystals, where molecules align along a common direction even though the material itself remains liquid.

The orchestra plays the symphony of climate. Each violin, each wind instrument carries its own part: these are the Kolmogorov modes, the system's natural rhythms. Suddenly, a thunderclap bursts into the hall: a sharp jump, like a gust of wind or a downpour. Previously, we could only listen to the smooth sound, but we couldn't decipher such chords. In the new work, mathematicians have completed the score.

A fisherman pulls on his net and listens to it ring. Each strand quivers in its own way, but before a strong tug, all the strands begin to vibrate in unison. So it is with complex systems: before a sharp state jump, the individual parts suddenly start to oscillate in concert, and that synchrony betrays the coming jump.