Minimisation of a Free-Energy-Like Potential for Non-Equilibrium Systems at Steady State

TL;DR

This paper introduces a new potential function for non-equilibrium systems that explains steady states through a variational principle, linking flux variability, entropy production, and phenomena like turbulence and ecological coexistence.

Contribution

It formulates a dimensionless potential analogous to free energy, deriving the maximum entropy production principle conditionally for non-equilibrium steady states.

Findings

Steady states correspond to minima of the potential function.

High flux variability is characteristic of the steady states.

The formulation explains phenomena like turbulence and ecological coexistence.

Abstract

This study examines a new formulation of non-equilibrium thermodynamics, which gives a conditional derivation of the ``maximum entropy production'' (MEP) principle for flow and/or chemical reaction systems at steady state. The analysis uses a dimensionless potential function $\phi_{st}$ for non-equilibrium systems, analogous to the free energy concept of equilibrium thermodynamics. Spontaneous reductions in $\phi_{st}$ arise from increases in the ``flux entropy'' of the system - a measure of the variability of the fluxes - or in the local entropy production; conditionally, depending on the behaviour of the flux entropy, the formulation reduces to the MEP principle. The inferred steady state is also shown to exhibit high variability in its instantaneous fluxes and rates, consistent with the observed behaviour of turbulent fluid flow, heat convection and biological systems; one consequence is the coexistence of energy producers and consumers in ecological systems. The different paths for attaining steady state are also classified.