# Classical chaos at finite temperature

Is there any finite temperature generalization of classical chaos? In quantum chaos, at least with regards to out-of-time-order correlators, the generalization is clear - one simply takes a thermal average instead of averaging over all states equally. However, I was unable to find any references regarding classical analogies to this. Does such a field exist? Is there an intuitive picture as to how the standard notion of classical chaos (something like the butterfly effect, where two states that are close together in phase space diverge exponentially) can generalize to finite temperature?

• I may be missing something obvious here, but I don't understand what you mean with "finite temperature generalization". Does the standard concept apply only to zero/infinite temperature systems? In which sense? – stafusa Mar 25 '19 at 1:16
• Sorry, I suppose the term "finite temperature" is a carry-over from quantum chaos. In classical chaos, there isn't a notion of temperature at all, which was my point (as opposed to QM, where not talking about temperature is usually equivalent to either zero or infinite temperature ensemble averages) – Henry Shackleton Mar 25 '19 at 12:40
• It's unfortunate no one is answering this question. – stafusa Mar 29 '19 at 1:05