Mean-Field “Temperature” in Far From Equilibrium Systems

We calculate the nonequilibrium mean-field "temperature" of a brownian system in contact with a heat bath. We consider two different cases: an equilibrium bath in the presence of strong external forces, and a nonequilibrium bath. By proving the existence of a generalized fluctuation-dissipation relation, this mean-field "temperature" can be used to describe a nonequilibrium system as is if it were in thermal equilibrium with a thermal bath at the mean-field "temperature" mentioned above. We apply our results to chemical reactions in the presence of external forces showing how chemical equilibrium and Kramers rate constants are modified by the presence of these forces.