Dissipation and the relaxation to equilibrium
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Using the recently derived dissipation theorem and a corollary of the transient fluctuation theorem (TFT), namely the second-law inequality, we derive the unique time independent, equilibrium phase space distribution function for an ergodic Hamiltonian system in contact with a remote heat bath. We prove under very general conditions that any deviation from this equilibrium distribution breaks the time independence of the distribution. Provided temporal correlations decay, we show that any nonequilibrium distribution that is an even function of the momenta eventually relaxes (not necessarily monotonically) to the equilibrium distribution. Finally we prove that the negative logarithm of the microscopic partition function is equal to the thermodynamic Helmholtz free energy divided by the thermodynamic temperature and Boltzmann's constant. Our results complement and extend the findings of modern ergodic theory and show the importance of dissipation in the process of relaxation toward equilibrium.
Journal of Statistical Mechanics: Theory and Experiment
Copyright 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. along with the following message: The following article appeared in J. Chem. Phys. 128, 014504 (2008) and may be found at http://dx.doi.org/10.1063/1.2812241
Thermodynamics and Statistical Physics