Article ID Journal Published Year Pages File Type
5372823 Chemical Physics 2016 14 Pages PDF
Abstract
The probability distributions, as well as the mean values of stochastic currents and fluxes, associated with a driven Langevin process, provide a good and topologically protected measure of how far a stochastic system is driven out of equilibrium. By viewing a Langevin process on a compact oriented manifold of arbitrary dimension m as a theory of a random vector field associated with the environment, we are able to consider stochastic motion of higher-dimensional objects, which allow new observables, called higher-dimensional currents, to be introduced. These higher dimensional currents arise by counting intersections of ak-dimensional trajectory, produced by a evolving (k-1)-dimensional cycle, with a reference cross section, represented by a cycle of complimentary dimension (m-k). We further express the mean fluxes in terms of the solutions of the Supersymmetric Fokker-Planck (SFP), thus generalizing the corresponding well-known expressions for the conventional currents.
Related Topics
Physical Sciences and Engineering Chemistry Physical and Theoretical Chemistry
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