Stochastic Thermodynamics of oscillators networks

TL;DR

This paper develops a general stochastic thermodynamics framework for complex oscillator networks, enabling calculation of thermodynamic quantities and analyzing non-equilibrium behaviors in various physical systems.

Contribution

It introduces a novel, general method to compute thermodynamic currents and entropy production in nonlinear oscillator networks, extending the understanding of non-potential forces and broken detailed balance.

Findings

Derived a formula for entropy production in oscillator networks.

Applied the formalism to ferromagnets, spin-oscillator networks, and nano friction models.

Demonstrated the breaking of detailed balance and time reversal symmetry far from equilibrium.

Abstract

We apply the stochastic thermodynamics formalism to describe the dynamics of systems of complex Langevin and Fokker-Planck equations. We provide in particular a simple and general recipe to calculate thermodynamical currents, dissipated and propagating heat for networks of nonlinear oscillators. By using the Hodge decomposition of thermodynamical forces and fluxes, we derive a formula for entropy production that generalises the notion of non-potential forces and makes trans- parent the breaking of detailed balance and of time reversal symmetry for states arbitrarily far from equilibrium. Our formalism is then applied to describe the off-equilibrium thermodynamics of a few examples, notably a continuum ferromagnet, a network of classical spin-oscillators and the Frenkel-Kontorova model of nano friction.