Energy fluctuations in simple conduction models

We introduce a class of stochastic weakly coupled map lattices, as models for studying heat conduction in solids. Each particle on the lattice evolves according to an internal dynamics that depends on its energy, and exchanges energy with its neighboors at a rate that depends on its internal state. We study energy fluctuations at equilibrium in a diffusive scaling. In some cases, we derive the hydordynamic limit of the fluctuation field.