The Principle of Minimal Resistance in Non-Equilibrium Thermodynamics

TL;DR

This paper reviews a global path integration approach to non-equilibrium thermodynamics, revealing a minimum resistance principle where dissipative systems tend to minimize energy dissipation during evolution.

Contribution

It introduces a global description based on path integration that generalizes local approaches like Langevin and Fokker-Planck equations, establishing a minimum resistance principle in non-equilibrium thermodynamics.

Findings

Dissipative systems tend to minimize energy dissipation during evolution.

The minimum resistance principle is valid under broad conditions.

Results align with classical equations like Fokker-Planck and Langevin in specific cases.

Abstract

Analytical models describing the motion of colloidal particles in given velocity fields are presented. In addition to local approaches, leading to well known master equations such as the Langevin and the Fokker-Planck equations, a global description based on path integration is reviewed. This shows that under very broad conditions, during its evolution a dissipative system tends to minimize its energy dissipation in such a way to keep constant the Hamiltonian time rate, equal to the difference between the flux-based and the force-based Rayleigh dissipation functions. At steady state, the Hamiltonian time rate is maximized, leading to a minimum resistance principle. In the unsteady case, we consider the relaxation to equilibrium of harmonic oscillators and the motion of a Brownian particle in shear flow, obtaining results that coincide with the solution of the Fokker-Planck and the Langevin equations.