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We investigate the dynamics of thermal Casimir interactions between platesdescribed within a living conductor model, with embedded mobile anions andcations, whose density field obeys a stochastic partial differential equationwhich can be derived starting from the Langevin equations of the individualparticles. This model describes the thermal Casimir interaction in the same waythat the fluctuating dipole model describes van der Waals interactions. Themodel is analytically solved in a Debye-H\"uckel-like approximation. Weidentify several limiting dynamical regimes where the time dependence of thethermal Casimir interactions can be obtained explicitly. Most notably we find aregime with diffusive scaling, even though the charges are confined to theplates and do not diffuse into the intervening space, which makes the diffusivescaling difficult to anticipate and quite unexpected on physical grounds.

Relaxation of the thermal Casimir force between net neutral plates containing Brownian charges