Thermodynamic Induction Effects Exhibited in Nonequilibrium Systems with Variable Kinetic Coefficients

TL;DR

This paper develops a nonequilibrium thermodynamic theory showing that variable kinetic coefficients can induce nonlinear effects, including self-organization and enhanced stability, with results supported by a variational approach.

Contribution

It introduces a thermodynamic induction effect in systems with variable kinetic coefficients, expanding understanding of nonlinear stability and self-organization in nonequilibrium thermodynamics.

Findings

Induction effect proportional to the square of the driving force.

Enhanced stability of stationary states due to nonlinear terms.

Potential for self-organization in systems with variable kinetic coefficients.

Abstract

A nonequilibrium thermodynamic theory demonstrating an induction effect of a statistical nature is presented. We have shown that this thermodynamic induction can arise in a class of systems that have variable kinetic coefficients (VKC). In particular if a kinetic coefficient associated with a given thermodynamic variable depends on another thermodynamic variable then we have derived an expression that can predict the extent of the induction. The amount of induction is shown to be proportional to the square of the driving force. The nature of the intervariable coupling for the induction effect has similarities with the Onsager symmetry relations, though there is an important sign difference as well as the magnitudes not being equal. Thermodynamic induction adds nonlinear terms that improve the stability of stationary states, at least within the VKC class of systems. Induction also produces a term in the expression for the rate of entropy production that could be interpreted as self-organization. Many of these results are also obtained using a variational approach, based on maximizing entropy production, in a certain sense. Non-equilibrium quantities analogous to the free energies of equilibrium thermodynamics are introduced.