The role of the nature of the noise in the thermal conductance of   mechanical systems
  Focussing on a paradigmatic small system consisting of two coupled damped oscillators, we survey the role of the L\'evy-It\^o nature of the noise in the thermal conductance. For white noises, we prove that the L\'evy-It\^o composition (Lebesgue measure) of the noise is irrelevant for the thermal conductance of a non-equilibrium linearly coupled chain, which signals the independence between mechanical and thermodynamical properties. On the other hand, for the non-linearly coupled case, the two types of properties mix and the explicit definition of the noise plays a central role. 
Welles A. M. Morgado, Silvio M. Duarte Queiros
cond-mat.stat-mech math-ph math.MP