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.