# Does it take the same amount of time, it takes for a system to get to a low-entropy (fluctuation) state from equilibrium, to go in the other way?

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?

• 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. – Wolpertinger Jan 30 '16 at 0:49
• @Numrok: You meant to say in equilibrium, there can be fluctuations? – user36790 Jan 30 '16 at 4:21
• 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. – Wolpertinger Jan 30 '16 at 7:35
• @Numrok: I thought the equilibrium is the largest entropic state. – user36790 Jan 30 '16 at 7:43
• it is, but entropy is also a macroscopic property. In fact entropy is defined through the possible microscopic configurations. – Wolpertinger Jan 30 '16 at 7:44