Nonequilibrium Energy Profiles for a Class of 1-D Models
  As a paradigm for heat conduction in 1 dimension, we propose a class of models represented by chains of identical cells, each one of which containing an energy storage device called a "tank". Energy exchange among tanks is mediated by tracer particles, which are injected at characteristic temperatures and rates from heat baths at the two ends of the chain. For stochastic and Hamiltonian models of this type, we develop a theory that allows one to derive rigorously -- under physically natural assumptions -- macroscopic equations for quantities related to heat transport, including mean energy profiles and tracer densities. Concrete examples are treated for illustration, and the validity of the Fourier Law in the present context is discussed. 
Jean-Pierre Eckmann, Lai-Sang Young