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According to statistical mechanics, micro-states of an isolated physical system (say, a gas in a box) at time $t_0$ in a given macro-state of less-than-maximal entropy typically evolve in such a way that the entropy at time $t$ increases with $|t-t_0|$ in both time directions.
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S. Goldstein, R. Tumulka, and N. Zanghì: From Infinity to Here: The Arrow of Time Without a Past Hypothesis. In preparation (2016)
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