Large Interconnected Thermodynamic Systems Nearly Minimize Entropy Production

TL;DR

This paper derives the minimum entropy production condition for nonequilibrium systems using stochastic thermodynamics and finds that large interconnected systems tend to minimize entropy production, indicating self-organization.

Contribution

It introduces a new derivation of the minimum entropy production state for Markov chains and shows large systems tend toward this minimum, challenging previous principles.

Findings

Large systems tend toward minimum entropy production as size increases.

Real nonequilibrium steady states often violate maximum or minimum entropy principles.

Numerical sampling supports convergence toward minimum entropy production in large interconnected systems.

Abstract

Many have speculated whether nonequilibrium systems obey principles of maximum or minimum entropy production. In this work, we use stochastic thermodynamics to derive the condition for the minimum entropy production state (MEPS) for continuous-time Markov chains (CTMCs), even far from equilibrium. We show that real nonequilibrium steady states (NESS) generally violate both the MINEP and MAXEP principles. However, through numerical sampling of large interconnected CTMCs, we find that as system size increases, the steady-state entropy production tends to converge toward the minimum. This suggests that large nonequilibrium systems may self-organize to make efficient use of thermodynamic resources, offering a nuanced perspective on the longstanding debate between MAXEP and MINEP.