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.
Highlights
This paper presents a critical review of several claims regarding Ziegler’s principle [1], the most basic and uncontroversial formulation of a maximum principle for the entropy production
maximum entropy production (MaxEP) is a broad collection of principles that do not necessarily match with each other and do not comply with the physical intuition encoded in the principle of minimum entropy production (MinEP), which is widely agreed to characterize steady states of systems subject to slightly off-equilibrium constraints, again, despite longstanding controversies
The kind of proposition that we address is “the steady state of open thermodynamic systems with sufficient degrees of freedom are maintained in a state at which the production of entropy is maximized given the constraints of the system” [26]
Summary
This paper presents a critical review of several claims regarding Ziegler’s principle [1], the most basic and uncontroversial formulation of a maximum principle for the entropy production. Our main theses are: Ziegler’s principle implies reciprocal relations between currents and forces (Sections 2 and 3). According to the former, the variable quantities are the response coefficients at fixed external forces, given the steady state; response relations follow. MaxEP is a constitutive principle that makes a statement about how the microphysics of the problem and the network topology affect the “inertia” of a system, while MinEP is a principle prescribing the behavior of states under given phenomenological laws. By “stationary” (denoted with ∗ ), we mean extremal solutions of a variational principle, while “steady” (denoted with (s) ) designates a configuration of currents that obeys Kirchhoff’s current law
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