Non-equilibrium steady states for networks of oscillators. (English) Zbl 1397.82033
Summary: 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.
MSC:
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 34C15 | Nonlinear oscillations and coupled oscillators for ordinary differential equations |
| 60B10 | Convergence of probability measures |
| 37A60 | Dynamical aspects of statistical mechanics |
Keywords:
non-equilibrium statistical mechanics; networks of oscillators; geometric ergodicity; Hörmander’s condition; Lyapunov functionsReferences:
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