Superconducting correlations and the thermodynamics of Josephson junctions

The rapid increase of the Josephson free energy as the temperature of a tunneling junction drops below the superconducting transition temperature T-c is shown to make this transition of first order if the phase difference across the junction is constrained to have a nonzero value. Taking this effect into account, we prove the existence of an availability potential governing the nonisothermal dynamics of the junction which, in contrast with previously published results, has no unphysical features like latent heat being released upon entering the - high temperature - normal state or a value in this normal state which depends on the - superconducting - phase difference. In a model of two ideal BCS superconductors coupled by a tunneling Hamiltonian the nonvanishing of the Josephson internal energy (and entropy) for T up arrow T-c is shown to be a consequence of superconducting correlations which (as finite-size corrections) persist even in the thermodynamic limit in the mean field BCS model. The classical counterpart of these correlations is investigated in detail in a mean field spin model of a Josephson junction, for which finite-size corrections to the free energy are shown to be expressible in terms of bulk quantities only.