Nonequilibrium work by charge control in a Josephson junction

Abstract

We consider a single Josephson junction in the presence of time varying gate charge, and examine the nonequilibrium work done by the charge control in the framework of fluctuation theorems. Assuming first a high quality junction with negligible Ohmic current, we obtain the probability distribution functions of the work and confirm the Crooks relation to give the estimation of the free energy changes ΔF=0. The reliability of ΔF estimated from the Jarzynksi equality is crucially dependent on protocol parameters, while the Bennett's acceptance ratio method yields consistently ΔF=0. We examine the behaviors of the work average and point out its relation to heat and entropy production associated with the circuit control. Finally considering finite tunnel resistance we discuss dissipation effects on the work statistics.