A Principled Basis for Nonequilibrium Stochastic Dynamics

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 (CFT), replacing state entropies with path entropies; and replacing (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 Fluctuation-Response and Maxwell-Onsager relations, applicable far from equilibrium; (ii) It constructs dynamical models from mixed force-observable constraints; and (iii) It reveals 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. CFT synthesizes and extends frameworks like Stochastic Thermodynamics, Large Deviation Theory, and the Maximum Caliber Principle, and it provides a foundation for understanding evolutionary optimization, control, and design.