The non-equilibrium steady state of sparse systems with non-trivial topology
Department of Physics, Ben-Gurion University of the Negev - Beer-Sheva 84105, Israel
2 Schulich Faculty of Chemistry, Technion - Israel Institute of Technology - Haifa 32000, Israel
Accepted: 16 March 2012
We study the steady state of a multiply connected system that is driven out of equilibrium by a sparse perturbation. The prototype example is an N-site ring coupled to a thermal bath, driven by a stationary source that induces transitions with log-wide distributed rates. An induced current arises, which is controlled by the strength of the driving, and an associated topological term appears in the expression for the energy absorption rate. Due to the sparsity, the crossover from linear response to saturation is mediated by an intermediate regime, where the current is exponentially small in , which is related to the work of Sinai on “random walk in a random environment”.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.70.Ln – Nonequilibrium and irreversible thermodynamics / 73.23.-b – Electronic transport in mesoscopic systems
© EPLA, 2012