Temperature Profiles in Hamiltonian Heat Conduction

We study heat transport in the context of Hamiltonian and related stochastic models with nearest-neighbor coupling, and derive a universal law for the temperature profiles of a large class of such models. This law contains a parameter $\alpha$, and is linear only when $\alpha =1$. The value of $\alpha$ depends on energy-exchange mechanisms, including the range of motion of tracer particles and their times of flight.