Maximum caliber is a general variational principle for nonequilibrium statistical mechanics

TL;DR

Maximum Caliber is proposed as a comprehensive variational principle for non-equilibrium statistical mechanics, capable of deriving known near-equilibrium results and extending to far-from-equilibrium systems without relying on traditional assumptions.

Contribution

The paper demonstrates that Max Cal serves as a unifying variational principle applicable to diverse non-equilibrium systems, extending beyond traditional thermodynamic constraints.

Findings

Max Cal reproduces Green-Kubo and Onsager relations near equilibrium.

Max Cal generalizes to far-from-equilibrium conditions.

Applicable to networks and non-material systems.

Abstract

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. More importantly, because Max Cal does not require any notion of 'local equilibrium', or any notion of entropy dissipation, or even any restriction to material physics, it is more general than many traditional approaches. We develop some generalizations of the Onsager and Prigogine results that apply arbitrarily far from equilibrium. Max Cal is not limited to materials and fluids; it also applies, for example, to flows and trafficking on networks more broadly.