Fact-checking Ziegler's maximum entropy production principle beyond the linear regime and towards steady states

TL;DR

This paper critically examines the maximum entropy production principle beyond linear regimes, showing it does not universally determine steady states and revealing limitations of Ziegler's principle in complex systems.

Contribution

The paper challenges the universality of the maximum entropy production principle and clarifies the roles of different thermodynamic principles in reaching steady states.

Findings

Ziegler's orthogonality leads to restrictive reciprocal relations.

A stochastic thermodynamics model violates these reciprocal relations.

Maximization of entropy production does not cause steady state onset, which is due to minimum entropy production.

Abstract

We challenge claims that the principle of maximum entropy production produces physical phenomenological relations between conjugate currents and forces, even beyond the linear regime, and that currents in networks arrange themselves to maximize entropy production as the system approaches the steady state. In particular: (1) we show that Ziegler's principle of thermodynamic orthogonality leads to stringent reciprocal relations for higher order response coefficients, and in the framework of stochastic thermodynamics, we exhibit a simple explicit model that does not satisfy them; (2) on a network, enforcing Kirchhoff's current law, we show that maximization of the entropy production prescribes reciprocal relations between coarse-grained observables, but is not responsible for the onset of the steady state, which is rather due to the minimum entropy production principle.