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Of the qualitative interpretations of entropy proposed, say, as a measure of "uncertainty," "randomness," "disorder," "unavailable energy," etc. of the system, are you aware of entropy being also (or alternatively) viewed as a measure of the "instability" of the realized microstate vis-a-vis all other possible microstates, for a given macrostate? Is this a meaningful way of looking at entropy?

I have a sense of how naive and vague my question is. But allow me to dwell on it a little more. My understanding is that a system (say, a simple one, ideal gas, etc.) with low entropy is off equilibrium ("unstable") and it will tend to move in the direction of maximum entropy. Equilibrium ("stability" for the system) is achieved at max entropy. (And I know that, in dynamics, stability has a more precise meaning.)

However, my question is not about the "stability" of the system. Instead, it is about the stability of a particular realized microstate vis-a-vis the other possible ones in the multiplicity, for a given macrostate. In a state of equilibrium (max entropy), there are so many other possible micro configurations of the system, the fact that one of these micro configurations is realized appears as a highly arbitrary or accidental event, the more so, the higher the multiplicity. One would think a tiny disturbance would suffice to switch the system to a different micro configuration, compatible with the given macrostate.

I'll appreciate comments and pointers to papers or books discussing this line of interpretation. Thanks in advance.

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Most likely I misunderstand your question:

One would think a tiny disturbance would suffice to switch the system to a different micro configuration, compatible with the given macrostate.

What you describe is actually what is happening at thermal equilibrium.

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  • $\begingroup$ One of my concerns is whether this interpretation I'm floating -- of entropy as micro "instability" for a given macro state -- implies a transition over time, while in my understanding equilibrium (max entropy state) refers to a point-in-time state. Hope this helps to clarify my question. $\endgroup$ – Julio Huato Feb 28 '18 at 19:57
  • $\begingroup$ Julio: equilibrium refers to a macrostate, but the macrostate could be in any of the compatible microstates. Is what I have learnt. Edit: aha, you want to know the microstate transitions that occur given a equilibrium macrostate, and if this relates to the entropy measure? $\endgroup$ – Emil Mar 2 '18 at 6:13
  • $\begingroup$ Yes to your edit. In particular, is it okay to say that the fundamental assumption (equiprobability of microstates) imply that higher multiplicity and entropy means that, in equilibrium, the realized microstate could "more easily" transition to any alternative microstate? Cf. bit.ly/2F9swsg , p. 10, 1st paragraph. $\endgroup$ – Julio Huato Mar 2 '18 at 20:04

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