Duality and fluctuation relations for statistics of currents on cyclic graphs

Abstract

We consider stochastic motion of a particle on a cyclic graph with arbitrarily periodic time dependent kinetic rates. We demonstrate duality relations for statistics of currents in this model and in its continuous version of a diffusion in one dimension. Our duality relations are valid beyond detailed balance constraints and lead to exact expressions that relate statistics of currents induced by dual driving protocols. We also show that previously known no-pumping theorems and some of the fluctuation relations, when they are applied to cyclic graphs or to one dimensional diffusion, are special consequences of our duality.

2 figure, 6 pages (In twocolumn). Accepted by JSTAT

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• Mimicking Nonequilibrium Steady States with Stochastic Pumps
• Geometric Heat Flux for Classical Thermal Transport in Interacting Open Systems
• Geometric Heat Pump: Controlling Thermal Transport with Time-dependent Modulations
• A proof by graphical construction of the no-pumping theorem of stochastic pumps
• Quantization and Fractional Quantization of Currents in Periodically Driven Stochastic Systems I: Average Currents
• Cycle Flux Ranking of Network Analysis in Quantum Thermal Device
• No-pumping theorem for many particle stochastic pumps
• Fluctuation Relations for Current Components in Mesoscopic Electric Circuits
• Hybrid models of molecular machines and the no-pumping theorem
• The validity of the no-pumping theorem in systems with finite-range interactions between particles