Rey-Bellet, Luc; Thomas, Lawrence E. Exponential convergence to non-equilibrium stationary states in classical statistical mechanics. (English) Zbl 0989.82023 Commun. Math. Phys. 225, No. 2, 305-329 (2002). Summary: We continue the study of a model for heat conduction [J.-P. Eckmann, C.-A. Pillet, and L. Rey-Bellet, Non-equilibrium statistical mechanics of anharmonic chains coupled to two heat baths at different temperatures, Commun. Math. Phys. 201, 657-697 (1999; Zbl 0932.60103)], consisting of a chain of nonlinear oscillators coupled to two Hamiltonian heat reservoirs at different temperatures. We establish existence of a Lyapunov function for the chain dynamics and use it to show exponentially fast convergence of the dynamics to a unique stationary state. Ingredients of the proof are the reduction of the infinite dimensional dynamics to a finite-dimensional stochastic process as well as a bound on the propagation of energy in chains of anharmonic oscillators. Cited in 45 Documents MSC: 82C05 Classical dynamic and nonequilibrium statistical mechanics (general) Keywords:model for heat conduction; Lyapunov function; chain dynamics Citations:Zbl 0932.60103 PDFBibTeX XMLCite \textit{L. Rey-Bellet} and \textit{L. E. Thomas}, Commun. Math. Phys. 225, No. 2, 305--329 (2002; Zbl 0989.82023) Full Text: DOI arXiv