Duality and fluctuation relations for statistics of currents on cyclic graphs

Details Duality and fluctuation relations for statistics of currents on cyclic graphs Duality and fluctuation relations for statistics of currents on cyclic graphs

2011-04-15

arxiv.org/abs/1104.2956v1

J. Stat. Mech. (2011) P05011

Physics

Condensed Matter

Statistical Mechanics

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

Scientific paper

10.1088/1742-5468/2011/05/P05011

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.

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