An Addendum to “Detailed Balance has a Counterpart in Nonequilibrium Steady States”

Transition rates in continuously driven steady states (relevant to sheared complex fluids) were derived in Evans (2004, 2005) by demanding that no information other than the microscopic laws of motion and the macroscopic observables of the system be used to describe it. This implies that the (nonequilibrium) reservoir, to which the system is weakly coupled, is fully characterized by its mean energy and mean flux. While we expect the resulting prescription for the rates in continuous- and discretized-time models to be equivalent, it is not trivial to see this from the expression for the rates derived in Evans (2005). We demonstrate this equivalence for a model of activated processes solved previously for continuous time (Evans 2005), thus demonstrating consistency of the theory.