Nonequilibrium temperatures in steady-state systems with conserved energy

We study a class of nonequilibrium lattice models describing local redistributions of a globally conserved quantity, which is interpreted as an energy. A particular subclass can be solved exactly, allowing us to define a statistical temperature T-th along the same lines as in the equilibrium microcanonical ensemble. We compute the response function and find that when the fluctuation-dissipation relation is linear, the slope T-FD(-1) of this relation differs from the inverse temperature T-th(-1). We argue that T-th is physically more relevant than T-FD, since in the steady-state regime, it takes equal values in two subsystems of a large isolated system. Finally, a numerical renormalization group procedure suggests that all models within the class behave similarly at a coarse-grained level, leading to a parameter that describes the deviation from equilibrium. Quantitative predictions concerning this parameter are obtained within a mean-field framework.