Phase-dependent electronic specific heat of mesoscopic Josephson junctions

We study the influence of superconducting correlations on the electronic specific heat in a diffusive superconductor-normal metal-superconductor Josephson junction. We present a description of this system in the framework of the diffusive-limit Green's function theory, taking into account finite temperatures, phase difference, as well as junction parameters. We find that proximity effect may lead to a substantial deviation of the specific heat compared to that in the normal state and that it can be largely tuned in magnitude by changing the phase difference between the superconductors. A measurement setup to confirm these predictions is also suggested.