Temperature in Nonequilibrium Systems with Conserved Energy

We study a class of nonequilibrium lattice models which describe local redistributions of a globally conserved energy. A particular subclass can be solved analytically, allowing us to define a temperature $T_{th}$ along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitly found to be linear, but its slope differs from the inverse temperature $T_{th}^{-1}$. A numerical renormalization group procedure suggests that, at a coarse-grained level, all models behave similarly, leading to a two-parameter description of their macroscopic properties.