Hopefully Anonymous: the usual phrasing is not “time-reversible” for that, as that can be interpreted as “the laws of physics are the same under exchange of t with -t”. One usual phrasing is “non-dissipative”, though I hold out for “retrodictable”. Even this isn’t sufficient for entropy to be conserved—what’s necessary is conservation of phase space volume. I’m going to cheese out and say that as energy conservation is enough to do this, that my comment about “reasonable” physics covers this.
But statistical mechanics can still treat the case where it isn’t. Yes, entropy can decrease. That violates the second law of thermodynamics. Note that it isn’t a law of statistical mechanics, and that we do in fact observe entropy fluctuations that dip negative in real open systems, without making statistical mechanics inapplicable. Note also that at most one closed system exists—the universe itself.
Hopefully Anonymous: the usual phrasing is not “time-reversible” for that, as that can be interpreted as “the laws of physics are the same under exchange of t with -t”. One usual phrasing is “non-dissipative”, though I hold out for “retrodictable”. Even this isn’t sufficient for entropy to be conserved—what’s necessary is conservation of phase space volume. I’m going to cheese out and say that as energy conservation is enough to do this, that my comment about “reasonable” physics covers this.
But statistical mechanics can still treat the case where it isn’t. Yes, entropy can decrease. That violates the second law of thermodynamics. Note that it isn’t a law of statistical mechanics, and that we do in fact observe entropy fluctuations that dip negative in real open systems, without making statistical mechanics inapplicable. Note also that at most one closed system exists—the universe itself.