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(a) Plot of ln of the two sides of the ESFT, Eq. (4), for binned data with lines represent the expected behaviour. The agreement is extremely good. (b) and (c) Plot of the average instantaneous dissipation (Ω(Γ(t)), —) and the dissipation theorem (, - - -) with time (b) and the difference between the two functions bounded by the standard error of the difference (c). Only by plotting the difference, it is possible to observe the difference between the two functions. (d) Plot of the average of the total dissipation with time. In contrast with the instantaneous dissipation function, (b), the average of the total dissipation function is positive definite.
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Relaxation of a system to equilibrium is as ubiquitous, essential, and as poorly quantified as any phenomena in physics. For over a century, the most precise description of relaxation has been Boltzmann's H-theorem, predicting that a uniform ideal gas will relax monotonically. Recently, the relaxation theorem has shown that the approach to equilibrium can be quantified in terms of the dissipation function first defined in the proof of the Evans-Searles fluctuation theorem. Here, we provide the first demonstration of the relaxation theorem through simulation of a simple fluid system that generates a non-monotonic relaxation to equilibrium.
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