The Principle of Minimal Resistance in Non-Equilibrium Thermodynamics

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.

References in corpus (3)

• Steepest Entropy Ascent Model for Far-Non-Equilibrium Thermodynamics. Unified Implementation of the Maximum Entropy Production Principle
• Fact-checking Ziegler's maximum entropy production principle beyond the linear regime and towards steady states
• From Random Motion of Hamiltonian Systems to Boltzmann H Theorem and Second Law of Thermodynamics -- a Pathway by Path Probability