  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.
