  This paper studies a billiards-like microscopic heat conduction model, which
describes the dynamics of gas molecules in a long tube with thermalized
boundary. We numerically investigate the law of energy exchange between
adjacent cells. A stochastic energy exchange model that preserves these
properties is then derived. We further numerically justified that the
stochastic energy exchange model preserves the ergodicity and the thermal
conductivity of the original billiard model.
