И вдруг возникает какой-то напев

[egovoru]

Царапающим русское ухо словом «эмерджентность» («возникаемость») обозначают наличие у целого свойств, отсутствующих у составляющих его компонентов. Вроде бы все понятно, но меня смущает вот что. Возьмем, например, температуру: ею обладает любая совокупность молекул, достаточно большая для того, чтобы мы могли засунуть туда термометр, хотя у

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[egovoru]

Да, по соседней ветке тоже уже заметили, что кинетическую энергию одной молекулы можно в каком-то смысле считать ее температурой (с соответствующим коэффициентом), но все-таки обычно температура - это макроскопический термодинамический параметр и в этом смысле эмерджентный.

Вот здесь пишут так:

"For a single molecule that is in complete isolation, it is indeed generally not true (or at least not useful) to assign it a temperature, as others have said. Such a system would be more naturally described in the so-called microcanonical ensemble of thermodynamics, and since it can have a well-defined and conserved energy, the usual role of temperature in determining the probability of occupation of different energy states via a Boltzmann distribution is not relevant. Put simply, temperature is only relevant when there is uncertainty about how much energy a system has, which need not be true when it is isolated*.

However, things are different when you have a molecule in an open system, which can freely exchange energy with its surroundings, as is certainly the case for the specific example the OP has described. In this case, as long as the molecule is in equilibrium or quasi-equilibrium with its surroundings, it does indeed have a well-defined temperature. If there are no other relevant conserved quantities, the quantum state of the molecule is described by a diagonal density matrix in the single-particle energy basis that follows the Boltzmann distribution, ρ=Z−1e−βH. Practically speaking, this means that if you know that the molecule is at equilibrium with a given temperature, each time you measure it you can know, probabilistically, what the likelihood is that you will see it with a given energy.

*For completeness I will mention that some people have nevertheless tried to extend the idea of temperature to isolated systems, as the wiki mentions, but this temperature doesn't generally behave in the way you expect from open systems, and it isn't a very useful concept."