Non-Equilibrium Steady States for Networks of Oscillators

TL;DR

This paper extends the understanding of non-equilibrium steady states from simple oscillator chains to complex networks, proving existence, uniqueness, and exponential convergence under certain conditions.

Contribution

It generalizes previous results to more complex networks of oscillators, establishing fundamental properties of their steady states.

Findings

Existence and uniqueness of steady states in complex oscillator networks

Exponential convergence to steady states

Conditions on potentials ensuring stability

Abstract

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.