Absence of correlations in the energy exchanges of an exactly solvable model of heat transport with many degrees of freedom

A process based on the exactly solvable Kipnis--Marchioro--Presutti model of heat conduction [J. Stat. Phys. 27 65 (1982)] is described whereby lattice cells share their energies among many identical degrees of freedom while, in each cell, only two of them are associated with energy exchanges connecting neighbouring cells. It is shown that, up to dimensional constants, the heat conductivity is half the interaction rate, regardless of the degrees of freedom. Moreover, as this number becomes large, correlations between the energy variables involved in the exchanges vanish. In this regime, the process thus boils down to the time-evolution of the local temperatures which is prescribed by the discrete heat equation.