On the validity of entropy production principles for linear electrical circuits

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.Comment: 19 pages, 1 fi

On the affordances of the MaxEP principle

Optimality principles have long been popular in the natural sciences and enjoyed much successes in various applications. However these principles seem to be disparate, each applied in limited contexts and there are far too many of them causing some consternation among scientists and philosophers of science regarding the ad-hoc nature of the optimality arguments. In this paper, we discuss the Maximum entropy production (MaxEP) as a plausible over-arching principle to understand stable configurations in fluid mechanics and related problems. The MaxEP being based upon sound physical arguments and in the immutable laws of thermodynamics along with the fact that it has been successfully co-opted across disciplines makes it worthy of attention. We discuss various physical and metaphysical aspects of this principle and use it to analyze some model problems regarding patterns in particle sedimentation such as sedimentation of a particle in Newtonian and non-Newtonian fluids and stable deformation of a falling droplet