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Communication: Beyond Boltzmann's H-theorem: Demonstration of the relaxation theorem for a non-monotonic approach to equilibrium
1. K. Huang, Statistical Mechanics (Wiley, New York, 1963).
4. V. Arnold and A. Avez, Ergodic Problems of Classical Mechanics (Benjamin, New York, 1968).
5. J. Dorfman, An Introduction to Chaos in Nonequilibrium Statistical Mechanics (Cambridge University Press, Cambridge, England, 1999).
13.Conformal relaxation occurs when the non-equilibrium distribution is of the form (f(Γ, t) = exp ( − βH + λ(t)g(Γ))/Z, ∀t) and the deviation function, g, is a constant over the relaxation.
15. M. Allen and D. Tildesley, Computer Simulation of Liquids (Oxford University Press, Oxford, 1994).
16. D. Evans and G. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Cambridge Unviersity Press, Cambridge, England, 2008).
18.Simulation parameters: 50 fluid particles, 22 wall particles, Δt = 1 × 10−3, T = 1, ρ = 0.3, and 100 000 trajectories.
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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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