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This is only true for closed systems (having no entropy-adding or -subtracting flow of matter or energy across their boundaries), and within them, there are usu

This is only true for closed systems (having no entropy-adding or -subtracting flow of matter or energy across their boundaries), and within them, there are usually more high entropy states than low entropy ones, so, on average, its evolution is more likely to end up in a higher entropy state than the one it started from, than in a lower one.

Chinjut 7y ago
There's no time-asymmetry in the statement "There's so many more higher entropy states than lower entropy states", so one can't deduce a time-asymmetric statement like "Entropy increases as time goes forwards" from it. If I call two states S1 and S2, with S2 at a later time than S1, then BOTH are likely to be high-entropy, and neither has any particular reason to be higher entropy than the other, just by virtue of this paucity of low-entropy states reasoning. See Loschmidt's paradox (https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox).
- mannykannot 7y ago
  > There's no time-asymmetry in the statement "There's so many more higher entropy states than lower entropy states." That is a good point, but this is only one of the premises of the full argument for the origin of time's arrow (and it is the one that answers gowld's question). The other premise is that the universe started in a low-entropy state. This establishes a contingent asymmetry in time, in that there happens to have been one special time when entropy was at or near a minimum, and then the asymmetry in the outcome of processes, from the first premise, puts a rachet on the time axis, so to speak, so that complex things will not make round trips in time. That is my understanding of the argument as it is often presented (e.g. by Feynman, in the article here, and also in Carroll's talk, mentioned by nullspace above), and the article you link to presents the big bang as a valid resolution of Lochschmidt's paradox. Thanks for bringing Lochschmidt's paradox to my attention, I had not heard of it before.

Chinjut 7y ago

There's no time-asymmetry in the statement "There's so many more higher entropy states than lower entropy states", so one can't deduce a time-asymmetric statement like "Entropy increases as time goes forwards" from it. If I call two states S1 and S2, with S2 at a later time than S1, then BOTH are likely to be high-entropy, and neither has any particular reason to be higher entropy than the other, just by virtue of this paucity of low-entropy states reasoning. See Loschmidt's paradox (https://en.wikipedia.org/wiki/Loschmidt%27s_paradox https://en.wikipedia.org/wiki/Loschmidt%27s_paradox).

mannykannot 7y ago
> There's no time-asymmetry in the statement "There's so many more higher entropy states than lower entropy states." That is a good point, but this is only one of the premises of the full argument for the origin of time's arrow (and it is the one that answers gowld's question). The other premise is that the universe started in a low-entropy state. This establishes a contingent asymmetry in time, in that there happens to have been one special time when entropy was at or near a minimum, and then the asymmetry in the outcome of processes, from the first premise, puts a rachet on the time axis, so to speak, so that complex things will not make round trips in time. That is my understanding of the argument as it is often presented (e.g. by Feynman, in the article here, and also in Carroll's talk, mentioned by nullspace above), and the article you link to presents the big bang as a valid resolution of Lochschmidt's paradox. Thanks for bringing Lochschmidt's paradox to my attention, I had not heard of it before.