Electronic Journal of Probability

Non-equilibrium steady states for networks of oscillators

Noé Cuneo, Jean-Pierre Eckmann, Martin Hairer, and Luc Rey-Bellet

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Non-equilibrium steady states for chains of oscillators (masses) connected by harmonic and anharmonic springs and interacting with heat baths at different temperatures have been the subject of several studies. In this paper, we show how some of the results extend to more complicated networks. We establish the existence and uniqueness of the non-equilibrium steady state, and show that the system converges to it at an exponential rate. The arguments are based on controllability and conditions on the potentials at infinity.

Article information

Electron. J. Probab., Volume 23 (2018), paper no. 55, 28 pp.

Received: 16 January 2018
Accepted: 13 May 2018
First available in Project Euclid: 7 June 2018

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Zentralblatt MATH identifier

Primary: 82C05: Classical dynamic and nonequilibrium statistical mechanics (general) 60H10: Stochastic ordinary differential equations [See also 34F05] 34C15: Nonlinear oscillations, coupled oscillators 60B10: Convergence of probability measures

non-equilibrium statistical mechanics networks of oscillators geometric ergodicity Hörmander’s condition Lyapunov functions

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Cuneo, Noé; Eckmann, Jean-Pierre; Hairer, Martin; Rey-Bellet, Luc. Non-equilibrium steady states for networks of oscillators. Electron. J. Probab. 23 (2018), paper no. 55, 28 pp. doi:10.1214/18-EJP177. https://projecteuclid.org/euclid.ejp/1528358489

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