Weak coupling limits in a stochastic model of heat conduction
  We study the Brownian momentum process, a model of heat conduction, weakly coupled to heat baths. In two different settings of weak coupling to the heat baths, we study the non-equilibrium steady state and its proximity to the local equilibrium measure in terms of the strength of coupling. For three and four site systems, we obtain the two-point correlation function and show it is generically not multilinear. 
Frank Redig, Kiamars Vafayi
cond-mat.stat-mech math-ph math.MP math.PR