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Let a system be in a state of fluctuation - a state of low-entropy at $t_0\;.$

Then before and after a sufficiently large but finite time-interval, the system would again be at equilibrium.

As the number of particles $N$ gets larger and larger, probability of fluctuation becomes lesser and lesser.

Eventually the system takes huge amount of time to go back to a large fluctuation state from equilibrium - a high-entropic state.

However, once the system reaches a lower entropy state or fluctuation after a large amount of time $T$ from higher entropic state, would the system take the same huge amount of time $T$ to go back to the higher entropic state from the large-fluctuation state?

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  • $\begingroup$ Two comments: - as N gets larger, only the fractional fluctuations decrease, the absolute fluctuations still diverge. So to say "probability of fluctuation becomes less" is a bit vague, if not incorrect. - Also could you elaborate what you mean by a "state", a "fluctuation state" and "equilibrium". E.g. equilibrium is defined by it's microscopic fluctuations, so I'm not quite sure what your question is. $\endgroup$ – Wolpertinger Jan 30 '16 at 0:49
  • $\begingroup$ @Numrok: You meant to say in equilibrium, there can be fluctuations? $\endgroup$ – user36790 Jan 30 '16 at 4:21
  • $\begingroup$ yes, in thermodynamics, equilibrium or any "state" is a macroscopic property of the system. This means that the exact microscopic details can fluctuate, but the average properties are described by things like pressure, temperature etc. $\endgroup$ – Wolpertinger Jan 30 '16 at 7:35
  • $\begingroup$ @Numrok: I thought the equilibrium is the largest entropic state. $\endgroup$ – user36790 Jan 30 '16 at 7:43
  • $\begingroup$ it is, but entropy is also a macroscopic property. In fact entropy is defined through the possible microscopic configurations. $\endgroup$ – Wolpertinger Jan 30 '16 at 7:44

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