Stochastic dynamics of extended objects in driven systems: I. Higherdimensional currents in the continuous setting
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 higherdimensional objects, which allow new observables, called higherdimensional currents, to be introduced. These higher dimensional currents arise by counting intersections of a k 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 FokkerPlanck (SFP), thus generalizing the corresponding wellknown expressions for the conventional currents.
 Publication:

Chemical Physics
 Pub Date:
 December 2016
 DOI:
 10.1016/j.chemphys.2016.08.021
 arXiv:
 arXiv:1609.00336
 Bibcode:
 2016CP....481....5C
 Keywords:

 Physics  Chemical Physics;
 Mathematical Physics;
 82C31;
 82C05;
 55B45;
 55C05
 EPrint:
 doi:10.1016/j.chemphys.2016.08.021