  The Kipnis-Marchioro-Presutti (KMP) is a known model consisting on a
one-dimensional chain of mechanically uncoupled oscillators, whose interactions
occur via independent Poisson clocks: when a Poisson clock rings, the total
energy at two neighbors is redistributed uniformly at random between them.
Moreover, at the boundaries, energy is exchanged with reservoirs of fixed
temperatures. We study here a generalization of the KMP model by considering
different rates at energy is exchanged with the reservoirs, and we then prove
the existence of a phase transition for the heat flow.
