Macroscopic constraints for the minimum entropy production principle

TL;DR

This paper explores how macroscopic constraints influence the minimum entropy production principle in network-based systems, demonstrating that steady states minimize entropy production under certain conditions and relating this to classical thermodynamic principles.

Contribution

It identifies network observables as key constraints preventing relaxation to equilibrium and extends the minimum entropy production principle to master equation systems.

Findings

Steady states satisfy a minimum entropy production principle in the linear regime.

Application to master equations links to invariant state principles.

The principle aligns with Prigogine's original formulation in a simple example.

Abstract

In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum entropy production principle. The result is applied to master equation systems, opening a new path to a well-known version of the principle regarding invariant states. Moreover, with the aid of a simple example, the principle is shown to conform to Prigogine's original formulation. Finally, we discuss analogies and differences with a recently proposed maximum entropy production principle.