Maximum Caliber Principle derives Maxwell-Onsager reciprocal relations for Fundamental Observables and Forces in Nonequilibria*

A powerful concept of thermodynamic equilibria is Maxwell's reciprocal relations. They can give hard-to-measure information about important driving forces from easy-to-measure observables. It would be valuable to have corresponding reciprocal relations for nonequilibrium dynamics. While some efforts have been made in this direction in the fields of large deviation theory and stochastic thermodynamics, they are often ad-hoc and/or limited by idealized-reservoir assumptions. Here we derive general and foundational relations based on the nonequilibrium principle of Maximum Caliber. We define a set of non-degenerate observables of distribution and fluxes that parametrizes the full degrees of freedom of nonequilibria and show how their conjugated path entropic forces can be connected to those defined in stochastic thermodynamics. We illustrate the reciprocal relationships on toy models of molecular motors.