Energy and entropy on irreversible chemical reaction-diffusion systems with asymptotic stability

TL;DR

This paper investigates how entropy and free energy evolve in irreversible reaction-diffusion systems using a Lyapunov function linked to system eigenvalues, connecting thermodynamics with dynamical stability.

Contribution

It introduces a Lyapunov function based on eigenvalues to relate system stability with thermodynamic quantities, redefining chemical potentials in irreversible systems.

Findings

Lyapunov function depends on eigenvalues and eigenvectors

The approach aligns with Onsager's reciprocal relations

Demonstrates consistency with thermodynamic principles

Abstract

In the framework of irreversible thermodynamics, we study autonomous systems of reaction-diffusion equations to show how the entropy and free energy of an open and irreversible reactor depend on concentrations. To do this, we find a Lyapunov function that depends directly on the eigenvalues and eigenvectors of the linearized problem valid for linear and asymptotically stable systems. By suggesting the role of this Lyapunov function as internal free energy, we were able to reflect the properties of the dynamical system directly into the second law of thermodynamics making a redefinition of the chemical potentials. We demonstrate the consistency of our hypotheses with basic thermodynamic principles such as the proportionality between flows and forces proposed by Onsager, the spectral decomposition of entropy production and the Glansdorff-Prigogine evolution criterion of a thermodynamic system.