Nonequilibrium Thermodynamics of Mesoscopic Systems

The Markovian dynamics of a Brownian particle is derived in the case that the local temperature is a stochastic variable. The isolated mesoscopic particle plus environment system is analyzed in the microcanonical ensemble by means of nonlinear-process projection methods. The ensuing generalized Kramers FokkerPlanck equation involves a thermodynamic potential of mean force that is different from the canonical free energy, and the conditional entropy (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 systems. 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 T_c in a model of two BCS superconductors coupled by a tunneling Hamiltonian. The predicted periodic dependence of the junction's T_c as a function of the flux in the SQUID has meanwhile been confirmed experimentally.