Theoretical analysis of the fluctuation theorem applied to electric circuits

We carry out a theoretical analysis of the fluctuations in the Johnson - Nyquist noise in an RC electric circuit being driven by a non-ideal constant current source. Using the appropriate Langevin equation, we derive the fluctuation theorem for the system. This analysis exhibits some interesting features. Firstly, the average of the dissipation function is not necessarily just an instantaneous entropy production, i.e. the work being done on the circuit by the external power source divided by the ambient temperature. Secondly, by appropriate selection of the values for the circuit components, the transient response of the system can be made identical to the nonequilibrium steady state response. In the limit of an ideal current source, the average of the dissipation function reduces to the entropy production. Our analysis accurately reproduces published experimental results.