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.

Fokker-Planck Equation and Thermodynamic System Analysis

“…According to [15,16], cells' behavior could be seen as the consequence of the interplay and dynamic balance between pairs of opposite elements, that are in the present approach the cell system and its environment. In [23][24][25][26] it has been pointed out that the two principles, maximum of entropy generation and least action, can be seen as the same fundamental laws of nature. The natural behavior of the open systems could be thought as the decrease of free energy in the least time (minimum).…”

“…The Equation (25) shows the connection to efficiency η of the molecular machine and the probability distribution. We can argue that this probability distribution, is strongly related to molecular machines operations and would be different from normal and ill cell, being different the behaviour of the cells and their interactions with the environment.…”

Training Concept, Evolution Time, and the Maximum Entropy Production Principle

“…Different versions of the MEPP have been considered previously [4][5][6][7]. Some authors argued that the MEPP is not true [23][24][25][26][27][28]. However, according to Martyushev and Seleznev [21,29] all these claims refer to experiments which violate, in one way or another, some applicability conditions of the principle.…”

An Entropy-Based Damage Characterization

“…Forgetting these fundamental points has raised several questions about the validity of MEPP and therefore, misconceptions. Some of the critical discussions on validity and applicability of MEPP can be found in [67][68][69][70][71]. Martyushev and co-workers in several publications [64][65][66] have clarified the region of applicability of MEPP and enumerated its restrictions.…”