  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.
