Canonical formulation of Thermodynamics, and corresponding wave equation for far from equilibrium case

TL;DR

This paper develops a canonical formulation of thermodynamics that extends classical equations to far-from-equilibrium conditions, deriving a wave equation analogous to Schrödinger's and validating it with a particle in a box.

Contribution

It introduces a novel extension of the CPDQ principle to non-equilibrium thermodynamics, deriving new equations that unify thermodynamic evolution with quantum-like wave behavior.

Findings

Derived Schrödinger-like equation for non-equilibrium thermodynamics

Validated the formulation with thermal conductance in a particle in a box

Extended classical thermodynamic equations to far-from-equilibrium scenarios

Abstract

Lagrange and Hamilton equations for thermodynamic evolution near equilibrium as well as Schrodinger-like equation for the non-equilibrium case are obtained extending the CPDQ Principle (Constancy of the product momentum-oordinate uncertainty) to a new conjugate pair where the momentum f is the extension of the mechanical f=p.{\delta}q product for the case the coordinate q is not directly observable. Applied to the case of a particle in a one dimension box, the results are in agreement with reported calculated and measured thermal conductance.