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

## TL;DR

This paper proposes an experimental test to investigate how the relaxation properties of conduction electrons affect the Casimir pressure between metal plates at different temperatures, potentially distinguishing between theoretical models.

## Contribution

It introduces a method to measure nonequilibrium Casimir pressures with modified setups, highlighting the impact of electron relaxation properties and model dependence.

## Key findings

- Casimir pressure depends on the extrapolation model used for optical data.
- A temperature difference of 10 K can discriminate between theoretical predictions.
- Modified experimental setup can measure nonequilibrium effects with high confidence.

## Abstract

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.