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Communication: Maximum caliber is a general variational principle for nonequilibrium statistical mechanics
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See supplementary material at http://dx.doi.org/10.1063/1.4928193
for the time independence of Lagrange multipliers when fluxes are time independent, lack of higher order reciprocal relationships, and modified reciprocal relationships when fluxes have different parities.[Supplementary Material]
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There has been interest in finding a general variational principle for non-equilibrium statistical mechanics. We give evidence that Maximum Caliber (Max Cal) is such a principle. Max Cal, a variant of maximum entropy, predicts dynamical distribution functions by maximizing a path entropy subject to dynamical constraints, such as average fluxes. We first show that Max Cal leads to standard near-equilibrium results—including the Green-Kubo relations, Onsager’s reciprocal relations of coupled flows, and Prigogine’s principle of minimum entropy production—in a way that is particularly simple. We develop some generalizations of the Onsager and Prigogine results that apply arbitrarily far from equilibrium. Because Max Cal does not require any notion of “local equilibrium,” or any notion of entropy dissipation, or temperature, or even any restriction to material physics, it is more general than many traditional approaches. It also applicable to flows and traffic on networks, for example.
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