Thermal conductivity and local thermodynamic equilibrium of stochastic energy exchange models

In this paper we study macroscopic thermodynamic properties of a stochastic microscopic heat conduction model that is reduced from deterministic problems. Our goal is to numerically check how the `low energy site effect' inherited from the deterministic model would affect the macroscopic thermodynamic properties such as the thermal conductivity and the local thermodynamic equilibrium. After a series of numerical computations, our conclusion is that neither the thermal conductivity nor the existence of local thermodynamic equilibrium is qualitatively changed by this effect.