2014/11/30 by Noé Cuneo, Jean-Pierre Eckmann, J-P Eckmann +1 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chemistry #Degeneracy (biology) #Ergodic theory #Ergodicity #Exponential function #Invariant (physics) #Invariant measure #Irreducibility #Lyapunov function #Markov Chains and Monte Carlo Methods #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear system #Physics #Pure mathematics #Quantum chaos and dynamical systems #Quantum mechanics #Statistical physics #Steady state (chemistry) #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.1088/0951-7715/28/7/2397
v3: minor corrections to reflect the published version
openalex publication_date 2015/06/20 · arxiv created 2015/09/03 · arxiv updated 2015/09/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider a chain of three rotors (rotators) whose ends are coupled to stochastic heat baths. The temperatures of the two baths can be different, and we allow some constant torque to be applied at each end of the chain. Under some non-degeneracy condition on the interaction potentials, we show that the process admits a unique invariant probability measure, and that it is ergodic with a stretched exponential rate. The interesting issue is to estimate the rate at which the energy of the middle rotor decreases. As it is not directly connected to the heat baths, its energy can only be dissipated through the two outer rotors. But when the middle rotor spins very rapidly, it fails to interact effectively with its neighbours due to the rapid oscillations of the forces. By averaging techniques, we obtain an effective dynamics for the middle rotor, which then enables us to find a Lyapunov function. This and an irreducibility argument give the desired result. We finally illustrate numerically some properties of the non-equilibrium steady state.