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::::::::Non-equilibrium is characterized by some sequence of measurements drifting a significant 'distance' through phase space. The drift may involve repeated distinct visits of the whole-system instantaneous microstate to some region of phase space, but it must be evident that they are repeated distinct and separate visits, not just little excursions in a permanent and persistent hovering pattern. In general, for a non-equilibrium trajectory through the phase space of whole-system instantaneous microstates, over some long observation time interval <math>(t_{\mathrm{initial}},t_{\mathrm{final}})</math>, the trajectory will drift from some region <math>R_{\mathrm {initial}} \subset R_0</math> to some other region <math>R_{\mathrm {final}} \subset R_0</math>, with negligible overlap <math>R_{\mathrm {initial}} \cap R_{\mathrm{final}}</math>. Thermodynamic entropy does not apply here. Other so-called 'entropies' may be defined ''ad lib'', but they refer to some kind of 'time rate of entropy production'.[[User:Chjoaygame|Chjoaygame]] ([[User talk:Chjoaygame|talk]]) 20:09, 19 December 2020 (UTC)
:::::::::I think of it this way: It is an *assumption* that every trajectory will visit any neighborhood in phase space with a probability proportional to the "volume" of that neighborhood. This is just another way of saying that each microstate is equally probable. Phase space may be divided up into a large number of macrostates, each with their own information entropy. For systems with a large number of particles, the microstates corresponding to equilibrium macrostates hugely outnumber the volume of the nonequilibrium microstates combined. It follows that, starting from a nonequilibrium microstate, the trajectory will wander into the equilibrium macrostate region and practically never leave. Observationally, that is the signature of an equilibrium state - the macrostate is unchanging. Since the
== Outstanding questions ==
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