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Originally written by Student of Trinity:

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For every initial state with a log that evolves into a final state with a pile of ash, there is a time reversed image of that final state. (Basically, just reverse the velocity of every particle, and there is the image of your state under time reversal.) This time reversed image constitutes an initial state from which an ash pile would indeed 'unburn' into a log. So among all possible states of the stuff in our tank, 'ash piles that are about to unburn' are exactly as common as 'logs that are about to burn'.

This set of 'unburning ash pile' states is surely a minute fraction of the size (phase space volume) of the set of states that a human would recognize as 'ash pile states'. In this sense, ash piles that are about to unburn are miraculously rare among ash piles.

But we are still left with the puzzle of why 'logs that are about to burn', which are exactly as rare, among all possibilities, as 'ashes that are about unburn', should be no more than moderately less common, among typically encountered states, than ordinary 'ash piles'.

Which, alas, is disappointingly similar to the problem we started with.

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