Deriving the Forces of Nonequilibria from Two Laws

Abstract

Non-EQuilibrium (NEQ) statistical physics has not had the same general foundation as that of EQuilibrium (EQ) statistical physics, where forces are derived from potentials such as $1/T = \partial S/\partial U$, and from which other key mathematical relations follow. Here, we show how general NEQ principles can be derived from two corresponding laws. Maximizing path entropy replaces maximizing state entropy. Whereas EQ can entail observables $(U, V, N)$, dynamics has (node populations, edge traffic, cycle flux). We derive forces of NEQ, fluctuation-susceptibility equalities, Maxwell-Onsager-like symmetry relations, and we generalize to ``cost-benefit'' relations beyond just work and heat dissipation.