  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.

Statistical Mechanics;Soft Condensed Matter