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On the polynomial convergence rate to nonequilibrium steady states. (English) Zbl 1404.60105

Summary: We consider a stochastic energy exchange model that models the 1-D 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.”

MSC:

60J25 Continuous-time Markov processes on general state spaces
82C05 Classical dynamic and nonequilibrium statistical mechanics (general)
37N05 Dynamical systems in classical and celestial mechanics
60G07 General theory of stochastic processes
82C35 Irreversible thermodynamics, including Onsager-Machlup theory
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References:

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