Considering an old and recurrent problem of nonequilibrium statistical physics, namely, the microscopic study of the heat flow, we investigate the effects on the heat conduction due the addition of graded structures or long range interactions in some usual models given by chains of oscillators....

We address the analytical investigation of nontrivial properties of heat flow, starting from microscopic models of matter. We present an integral representation for the expression of the heat flow, by taking as our crystal model a self-consistent chain of anharmonic oscillators, precisely, a...