# Does the heat death of the universe really imply a maximum entropy state *all* of the time? Or most of the time?

Statistically speaking, you're going to still encounter deviations from equilibrium, even though the expected value is equilibrium. But these rare deviations from equilibrium - which are inevitable - might have the power to do work. So does the universe inevitably descend towards a maximum-entropy state? Or is it only probabilistically destined towards a maximum-entropy state - that is - it will be in that state more than any other state.

After all, someone has even hypothesized a Poincare recurrence time, as described below:

http://en.wikipedia.org/wiki/Timeline_of_the_far_future

Scale of an estimated Poincaré recurrence time for the quantum state of a hypothetical box containing an isolated black hole of stellar mass.[47] This time assumes a statistical model subject to Poincaré recurrence. A much simplified way of thinking about this time is that in a model in which history repeats itself arbitrarily many times due to properties of statistical mechanics, this is the time scale when it will first be somewhat similar (for a reasonable choice of "similar") to its current state again.

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I think you answered your own question. – Raskolnikov Oct 4 '11 at 18:32
I'd still like some clarification though. Especially since everyone else still seems to believe in the opposite – InquilineKea Oct 4 '11 at 18:41

## 1 Answer

You're right, this is not brought up nearly often enough: the second law of thermodynamics is only probabilistic. Entropy is directly related to the number of microstates that correspond to a given physical configuration by $S = k_B\ln\Omega$. Given that definition and the ergodic hypothesis, which says that a system samples all accessible microstates with equal probability, it's clear that a system will not spend all its time in the configuration with maximal entropy. And whenever it does reach that configuration, it won't stay there forever, which means that entropy necessarily has to decrease at some point.

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I remember the example of a checker board with black and white pawns,black and white in two places with respect to the board. Entropy introduces disorder... up to the point where the black pawns are on white squares and white pawns on black squares, and an order appears. – anna v Oct 5 '11 at 4:44