  We consider a stochastic energy exchange model that models the 1D microscopic
heat conduction in the nonequilibrium setting. In this paper, we prove the
existence and uniqueness of the nonequilibrium steady state (NESS) and,
furthermore, the polynomial speed of convergence to the NESS. Our result shows
that the asymptotic properties of this model and its deterministic dynamical
system origin are consistent. The proof uses a new technique called the induced
chain method. We partition the state space and work on both the Markov chain
induced by an "active set" and the tail of return time to this "active set".
