Numerical Test of the Onsager Relations in a Driven System.

The Onsager reciprocity relations were formulated in the context of irreversible thermodynamics, but they are based on assumptions that have a wider applicability. Here, we present simulations testing the Onsager relations between surface-coupled diffusive and bulk fluxes in a system prepared in a nonequilibrium steady state. The system consists of a mixture of two identical species maintained at different temperatures inside a channel. In order to tune the friction of the two species with the walls independently, while keeping the particle-wall interaction potentials the same, we allow the kinematics of particle-wall collisions to be different: "bounce-back" (B) or "specular" (S). In the BB case, diffusio-capillary transport can only take place if the two species have different temperatures. We find that the Onsager reciprocity relations are obeyed in the linear regime, even in the BB case where all fluxes are the result of perturbing the system from a nonequilibrium steady state in a way that does not satisfy time-reversal symmetry. Our Letter provides a direct, numerical illustration of the validity of the Onsager relations outside their original range of application, and suggests their relevance for transport in driven or active systems.