Long-time diffusion and energy transfer in polydisperse mixtures of particles with different temperatures

Abstract

Evidence suggests that the transport rate of a passive particle at long timescales is enhanced due to interactions with the surrounding active ones in a size- and composition-dependent manner. Using a system of particles with different temperatures, we probe these effects in dilute solutions and derive long-time friction and self-diffusion coefficients as functions of volume fractions, sizes and temperatures of particles in $d=2$ and 3 dimensions. Thus, we model excluded-volume interactions for nonequilibrium systems but also extend the scope to short-range soft potentials and compare our results to Brownian-dynamics simulations. Remarkably, we show that both viscosity and energy flux display a nonlinear dependence on size. The simplicity of our formalism allows to discover various interesting scenarios that can be relevant for biological systems and active colloids.

arXiv commentPublished version, main text and supplemental material

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• A Cold Tracer in a Hot Bath: In and Out of Equilibrium
• Statistical mechanics of a cold tracer in a hot bath
• Boundary-Induced Drift and Negative Mobility in Constrained Stochastic Systems