A principled basis for nonequilibrium network flows

The great power of equilibrium 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, μ). Here, we generalize this structure to nonequilibria in Caliber Force Theory, replacing state entropies with path entropies; and replacing (U, V, N) with dynamic observables (node probabilities, edge traffics, and cycle fluxes). Caliber Force Theory derives dynamical forces and a complete set of conjugate relations: (i) It yields generalized Maxwell-Onsager relations and fluctuation-response relations, applicable far from equilibrium; (ii) It constructs dynamical models from mixed force-observable constraints; and (iii) It reveals relationships—including a generalized Einstein relation, an “equal-traffic” rule for optimizing molecular motors, and a “third Kirchhoff’s law” of stochastic transport—and can resolve some dynamical paradoxes. Caliber Force Theory extends the thermodynamic structure of equilibrium statistical physics to nonequilibrium systems. The framework derives generalized conjugate relations and transport laws, offering a unified approach to modelling dynamics far from equilibrium.