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?