Jean-Pierre Eckmann, Lai-Sang Young
Nonequilibrium Energy Profiles for a Class of 1-D Models
(5292K, Postscript, PDF)

ABSTRACT.  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.