On the validity of entropy production principles for linear electrical circuits

TL;DR

This paper examines the validity of entropy production principles in linear electrical circuits near equilibrium, using fluctuation theory and Langevin equations to explain when and why these principles hold or fail.

Contribution

It provides a dynamical fluctuation theory framework to understand the conditions under which minimum and maximum entropy production principles are valid in electrical circuits.

Findings

Entropy production rate approximates the fluctuation functional near equilibrium.

Time-reversal properties of observables influence entropy production principles.

Landauer's counterexample is explained by odd parity of observables under time-reversal.

Abstract

We discuss the validity of close-to-equilibrium entropy production principles in the context of linear electrical circuits. Both the minimum and the maximum entropy production principle are understood within dynamical fluctuation theory. The starting point are Langevin equations obtained by combining Kirchoff's laws with a Johnson-Nyquist noise at each dissipative element in the circuit. The main observation is that the fluctuation functional for time averages, that can be read off from the path-space action, is in first order around equilibrium given by an entropy production rate. That allows to understand beyond the schemes of irreversible thermodynamics (1) the validity of the least dissipation, the minimum entropy production, and the maximum entropy production principles close to equilibrium; (2) the role of the observables' parity under time-reversal and, in particular, the origin of Landauer's counterexample (1975) from the fact that the fluctuating observable there is odd under time-reversal; (3) the critical remark of Jaynes (1980) concerning the apparent inappropriateness of entropy production principles in temperature-inhomogeneous circuits.