effective temperature

A superconductor is a material in which electricity flows without loss, like water through a perfectly smooth pipe. But if you squeeze it slightly, like a spring, its properties change. Scientists have long wanted to measure how much heat such a compressed material absorbs, but instruments couldn't fit into the cramped setup. Now they've devised a way around this obstacle.

Two black holes, caught in a dance, spiral closer and closer until they merge into one. This dance is not silent: it shakes spacetime itself, sending gravitational waves rippling across the Universe. To understand what we hear in these waves, we need a precise mathematical model of the dance.

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.

In an oven, as temperature rises, molecules move faster and disorder increases. With language models like ChatGPT, it's the opposite. When developers increase the 'temperature' parameter, the model gets access to a wider choice of words, but its long texts suddenly start looping. A team of researchers tested 11 different AIs by generating 12,000 text continuations.

A search party combs a foggy field. At first, people spread out wide: a high 'temperature' of search means a great variety of attempts. Upon finding a trace, they close in. But the speed of convergence is critical — narrow the circle too early, and the best find stays aside. The coordinator assesses the spread of searchers and commands when to speed up or slow down.

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.

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.

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.

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.

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.

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.

A heat engine doesn't have to be made of iron. In the microworld, a single electron can play the role of a piston, and the measurement process itself can serve as fuel. Two neighboring 'pockets' for electrons are connected by a narrow bridge.

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.

A hot chain of atoms lined up in a row behaves like a tiny black hole. Such a chain is a series of particles, each resembling a tiny magnet. At normal temperatures, the little magnets flip randomly, but when cooled, they align in a uniform order. Physicists have discovered that when heated, this simple system reproduces the strange properties of black holes.

A cell is a city where tiny motors work nonstop. They carry cargo, move cilia, and make muscles contract. All this work generates heat, just like a car engine warms up. But measuring the heat from a single motor a few nanometers in size is no easy task. Stochastic modeling helps us peek into this world.

A hot coffee cools by radiating invisible light. To maintain temperature, it must receive exactly as much light back. This silent trade of photons is what we feel as steady warmth.

Cooling usually brings order: water freezes into ice. But in the quantum world, order takes unexpected forms. Experimenters cooled polaritons — particles that are both light and matter — to near absolute zero.

Picture a chef flicking water onto a sizzling skillet. The droplets instantly hiss and evaporate, giving immediate feedback on the temperature — far quicker than any thermometer. This intuitive idea underpins a new approach in quantum thermometry.

Usually, we think of the number of dimensions as fixed: length, width, height. But in the quantum world, even that can be changeable. A new theory describes systems where dimension isn't a constant but a quantum property, capable of being different simultaneously. A balloon is flat when cold, round when warm.

The Mpemba paradox, hot water sometimes freezes faster than cold, has gained a quantum sequel. In the microworld, a particle pushed farther from the finish line gets there first. Experimenters demonstrated this on a single spin: like a racer, they pushed it farther from equilibrium, and it reached it faster than after a weak nudge.

Atoms, like a swarm of fireflies, shine in unison. When they flash together, the light multiplies — a hundred atoms shine ten thousand times brighter than one. Physicists have turned this trick into a heat engine. A typical motor needs both a hot and a cold source, but here the atoms operate with just a cold one.

Quantum entanglement is a fragile resource. Heat a system, and thermal fluctuations will tear the delicate threads of correlations: at a sufficiently high but finite temperature, the Gibbs state of a local Hamiltonian becomes separable, that is, representable as a probabilistic mixture of products of local states.

A thermometer dipped into a sample usually tells you only the temperature. But if the temperature oscillates slightly and the sample responds with a delay, that response hides more: the imaginary part of the heat capacity, which turns out to be able to hear the quantum echo of time.