Casimir pressure between metallic plates out of thermal equilibrium: Proposed test for the relaxation properties of free electrons

© 2019 American Physical Society. ©2019 American Physical Society. We propose a test on the role of relaxation properties of conduction electrons in the Casimir pressure between two parallel metal-coated plates kept at different temperatures. It is shown that for sufficiently thick metallic coatings the Casimir pressure and pressure gradient are determined by the mean of the equilibrium contributions calculated at temperatures of the two plates and by the term independent on separation. Numerical computations of the nonequilibrium pressures are performed for two parallel Au plates of finite thickness as a function of separation and temperature of one of the plates using the plasma and Drude models for extrapolation of the optical data of Au to low frequencies. The obtained results essentially depend on the extrapolation used. Modifications of the CANNEX setup, originally developed to measure the Casimir pressure and pressure gradient in thermal equilibrium, are suggested, which allow different temperatures of one of the plates. Computations of the nonequilibrium pressure and pressure gradient are performed for a realistic experimental configuration. According to our results, even with only a 10 K difference in temperature between the plates, the experiment could discriminate between different theoretical predictions for the total pressure and its gradient, as well as for the contributions to them due to nonequilibrium, at high confidence