Correlation and response in a driven dissipative model

We consider a simple dissipative system with spatial structure in contact with a heat bath. The system always exhibits correlations except in the cases of zero and maximal dissipation. We explicitly calculate the correlation function and the nonlocal response function of the system and show that they have the same spatial dependence. Finally, we examine heat transfer in the model, which agrees qualitatively with simulations of vibrated granular gases.