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We propose a test on the role of relaxation properties of conductionelectrons in the Casimir pressure between two parallel metal-coated plates keptat different temperatures. It is shown that for sufficiently thick metalliccoatings the Casimir pressure and pressure gradient are determined by the meanof the equilibrium contributions calculated at temperatures of the two platesand by the term independent on separation. Numerical computations of thenonequilibrium pressures are performed for two parallel Au plates of finitethickness as a function of separation and temperature of one of the platesusing the plasma and Drude models for extrapolation of the optical data of Auto low frequencies. The obtained results essentially depend on theextrapolation used. Modifications of the CANNEX setup, originally developed tomeasure the Casimir pressure and pressure gradient in thermal equilibrium, aresuggested, which allow different temperatures of one of the plates.Computations of the nonequilibrium pressure and pressure gradient are performedfor a realistic experimental configuration. According to our results, even withonly a 10~K difference in temperature between the plates, the experiment coulddiscriminate between different theoretical predictions for the total pressureand its gradient, as well as for the contributions to them due tononequilibrium, at high confidence.

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