A Principled Basis for Nonequilibrium Network Flows

TL;DR

This paper extends equilibrium statistical physics principles to nonequilibrium network flows using Caliber Force Theory, deriving new relations and models for dynamic systems far from equilibrium.

Contribution

It introduces Caliber Force Theory, generalizing equilibrium concepts to nonequilibrium networks with new relations and optimization rules.

Findings

Derives generalized Maxwell-Onsager relations for nonequilibrium systems

Constructs dynamical models from mixed constraints

Reveals new relationships like the 'equal-traffic' rule and 'third Kirchhoff's law'

Abstract

The great power of EQuilibrium (EQ) statistical physics comes from its principled foundations: its First Law (conservation), Second Law (variational tendency principle), and its Legendre Transforms from observables $(U, V, N)$ to their driving forces $(T, p, \mu)$. Here, we generalize this structure to Non-EQuilibria (NEQ) in \textit{Caliber Force Theory} (CFT), replacing state entropies with path entropies; and $(U, V, N)$ with dynamic observables (node probabilities, edge traffics, and cycle fluxes). CFT derives dynamical forces and a complete set of conjugate relations: (i) It yields generalized Maxwell-Onsager relations, applicable far from equilibrium; (ii) It constructs dynamical models from mixed force-observable constraints; and (iii) It reveals new relationships -- including an ``equal-traffic'' rule for optimizing molecular motors, and a ``third Kirchhoff's law'' of stochastic transport -- and can resolve some dynamical paradoxes.