Title: Diffusive contact between randomly driven colloidal suspensions

Abstract: We study the relaxation process of two driven colloidal suspensions in diffusive contact to a steady state, similar to thermalization. We start by studying a single suspension, subjecting it to random driving forces via holographic optical tweezers, which agitate it to a higher effective temperature. Interestingly, the effective temperature of the suspension, defined by the Einstein relation, exhibits a non-monotonic dependence on the driving frequency. Next, we follow the flux of particles between two such suspensions in diffusive contact, starting from a uniform density and relaxing to a state with zero net particle flux. The density remains uniform for systems with different frequencies but equal effective temperatures. At high driving frequencies, we show that the density distribution at steady state is determined by equating the ratio of the chemical potential to the effective temperature in both systems, mirroring thermal equilibrium behavior.