Gauge invariance and geometric phase in nonequilibrium thermodynamics

TL;DR

This paper establishes a connection between lattice gauge theories and nonequilibrium thermodynamics in oscillator networks, revealing how gauge fields influence energy flows and predicting persistent currents confirmed by simulations.

Contribution

It introduces a novel framework linking gauge invariance with thermodynamic forces in nonlinear oscillator networks, applicable far from equilibrium.

Findings

Persistent energy and particle currents circulate in the network.

Thermodynamic forces relate to the curvature of the gauge connection.

Numerical simulations confirm theoretical predictions.

Abstract

We show the link between U1 lattice gauge theories and the off-equilibrium thermodynamics of a large class of nonlinear oscillators networks. The coupling between the oscillators plays the role of a gauge field, or connection, on the network. The thermodynamical forces that drive energy flows are expressed in terms of the curvature of the connection, analogous to a geometric phase. The model, which holds both close and far from equilibrium, predicts the existence of persistent energy and particle currents circulating in close loops through the network. The predictions are confirmed by numerical simulations. Possible extension of the theory and experimental applications to nanoscale devices are briefly discussed.