Temperature in nonequilibrium systems with conserved energy

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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 to define a temperature Tth along the same lines as in the equilibrium microcanonical ensemble. The fluctuation-dissipation relation is explicitely found to be linear, but its slope differs from the inverse temperature Tth⁻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.