Nonequilibrium thermodynamics of mesoscopic systems

The Markovian dynamics of a Brownian particle is derived in the case that t he local temperature is a stochastic variable. The isolated mesoscopic "par ticle plus environment" system is analyzed in the microcanonical ensemble b y means of nonlinear-process projection methods, The ensuing generalized Kr amers Fokker-Planck equation involves a thermodynamic potential of mean for ce that is different from the canonical free energy, and the conditional en tropy (or availability) emerges as the relevant steady-state potential. By coupling the system to a heat bath, we provide a microscopic foundation for the phenomenological theory of nonisothermal activation in mesoscopic syst ems. In the second part of this article, we then prove the existence of an availability potential governing the nonisothermal features of a Josephson junction in a SQUID, by studying the Josephson internal energy (and entropy ) for T up arrow T-c in a model of two BCS superconductors coupled by a tun neling Hamiltonian. The predicted periodic dependence of I:he junction's T- c as a function of the flux in the SQUID has meanwhile been confirmed exper imentally.