Non-equilibrium steady state and subgeometric ergodicity for a chain of three coupled rotors

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 tha...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2015-07, Vol.28 (7), p.2397-2421
Main Authors: Cuneo, N, Eckmann, J-P, Poquet, C
Format: Article
Language:English
Subjects:
chain of rotors
Chains
Constants
convergence to steady state
Ergodic processes
Joining
Lyapunov functions
non-equilibrium
Oscillations
Rotors
Steady state
stochastic process
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/28/7/2397