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We discuss the validity of close-to-equilibrium entropy production principlesin the context of linear electrical circuits. Both the minimum and the maximumentropy production principle are understood within dynamical fluctuationtheory. The starting point are Langevin equations obtained by combiningKirchoff's laws with a Johnson-Nyquist noise at each dissipative element in thecircuit. The main observation is that the fluctuation functional for timeaverages, that can be read off from the path-space action, is in first orderaround equilibrium given by an entropy production rate. That allows tounderstand beyond the schemes of irreversible thermodynamics (1) the validityof the least dissipation, the minimum entropy production, and the maximumentropy production principles close to equilibrium; (2) the role of theobservables' parity under time-reversal and, in particular, the origin ofLandauer's counterexample (1975) from the fact that the fluctuating observablethere is odd under time-reversal; (3) the critical remark of Jaynes (1980)concerning the apparent inappropriateness of entropy production principles intemperature-inhomogeneous circuits.Comment: 19 pages, 1 fi

On the Validity of Entropy Production Principles for Linear Electrical Circuits