Non-equilibrium thermodynamics and Fisher information: An illustrative example

Abstract Both non-equilibrium and equilibrium thermodynamics can be obtained from a constrained Fisher extremization process whose output is a Schrodinger-like wave equation (SWE). Within this paradigm, equilibrium thermodynamics corresponds to the ground state (GS) solution, while non-equilibrium thermodynamics corresponds to admixtures of this GS with excited state solutions. The method is a new and powerful approach to off-equilibrium thermodynamics. We discuss an application to electrical conductivity processes, and thereby, by construction, show that the following three approaches yield identical results: (1) the conventional Boltzmann transport equation in the relaxation approximation, (2) the Rumer and Ryvkin Gaussian–Hermite-algorithm, and (3) our Fisher–Schrodinger technique.