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

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.

21 pages

References in corpus (4)

• A possible classification of nonequilibrium steady states
• A discussion on maximum entropy production and information theory
• Minimum entropy production principle from a dynamical fluctuation law
• An equivalence between a Maximum Caliber analysis of two-state kinetics and the Ising model

Cited by in corpus (5)

• The restrictions of the Maximum Entropy Production Principle
• Effective fluctuation and response theory
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• Multicyclic norias: a first-transition approach to extreme values of the currents
• The Principle of Minimal Resistance in Non-Equilibrium Thermodynamics