Open Access
2018 Non-equilibrium steady states for networks of oscillators
Noé Cuneo, Jean-Pierre Eckmann, Martin Hairer, Luc Rey-Bellet
Electron. J. Probab. 23: 1-28 (2018). DOI: 10.1214/18-EJP177


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.


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Noé Cuneo. Jean-Pierre Eckmann. Martin Hairer. Luc Rey-Bellet. "Non-equilibrium steady states for networks of oscillators." Electron. J. Probab. 23 1 - 28, 2018.


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

zbMATH: 1397.82033
MathSciNet: MR3814249
Digital Object Identifier: 10.1214/18-EJP177

Primary: 34C15 , 60B10 , 60H10 , 82C05

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

Vol.23 • 2018
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