The Mystery of Hidden Temperature express

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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.

The problem is that this "local" temperature cannot be measured directly: it is not tied to a single quantity that you can probe with an instrument. So scientists have to guess its distribution, which is unreliable. The authors of the new work found a way out: they showed that the hidden temperature can be linked to the system's energy. Energy can be measured, and thus temperature can be computed.

The authors tested their method on a concrete example — the so-called q-canonical ensemble, which describes systems with unusual statistics. They computed how temperature is distributed at a given energy and obtained the full distribution without complicated mathematical transformations. It's as if, instead of emptying the bag, you learned to determine the size of the candies by the sound they make when poured.

Now physicists have a tool to look inside complex non-equilibrium systems — from plasma in the lab to distant star clusters. And perhaps better understand how order emerges from chaos.