“conditional on any given (nonmaximal) level of entropy, the vast majority of states have increasing entropy”
I don’t think this statement can be true in any sense that would produce a non-symmetric behavior over a long time, and indeed it has some problem if you try to express it in a more accurate way: 1) what does “non-maximal” mean? You don’t really have a single maximum, you have a an average maximum and random oscillations around it 2) the “vast majority” of states are actually little oscillations around an average maximum value, and the downward oscillations are as frequent as the upward oscillations 3) any state of low entropy must have been reached in some way and the time needed to go from the maximum to the low entropy state should be almost equal to the time needed to go from the low entropy to the maximum: why shold it be different if the system has time symmetric laws?
In your graph you take very few time to reach low entropy states from high entropy—compared to the time needed to reach high entropy again, but would this make the high-low transition look more natural or more “probable”? Maybe it would look even more innatural and improbable!
“conditional on any given (nonmaximal) level of entropy, the vast majority of states have increasing entropy”
I don’t think this statement can be true in any sense that would produce a non-symmetric behavior over a long time, and indeed it has some problem if you try to express it in a more accurate way:
1) what does “non-maximal” mean? You don’t really have a single maximum, you have a an average maximum and random oscillations around it
2) the “vast majority” of states are actually little oscillations around an average maximum value, and the downward oscillations are as frequent as the upward oscillations
3) any state of low entropy must have been reached in some way and the time needed to go from the maximum to the low entropy state should be almost equal to the time needed to go from the low entropy to the maximum: why shold it be different if the system has time symmetric laws?
In your graph you take very few time to reach low entropy states from high entropy—compared to the time needed to reach high entropy again, but would this make the high-low transition look more natural or more “probable”? Maybe it would look even more innatural and improbable!