Maintaining the local critical temperature of thermally out-of-equilibrium superconducting wires below the critical value

A generalized theory of open quantum systems combined with mean-field theory is used to study a superconducting wire in contact with thermal baths at different temperatures. It is shown that, depending on the temperature of the colder bath, the temperature of the hotter bath can greatly exceed the equilibrium critical temperature, and still the wire remains in the superconducting state, meaning that the effective local temperature in the wire is maintained below the critical temperature. The effects of contact areas and disorder are studied. Finally, an experimental setup is suggested to test our predictions.