Stochastic Dynamics of Extended Objects in Driven Systems: I. Higher-Dimensional Currents in the Continuous Setting
arXiv:1609.00336 · doi:10.1016/j.chemphys.2016.08.021
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 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 Fokker-Planck (SFP), thus generalizing the corresponding well-known expressions for the conventional currents.
References in corpus (11)
- Non equilibrium steady states: fluctuations and large deviations of the density and of the current
- Fluctuation theorems for stochastic dynamics
- Nonequilibrium Detailed Fluctuation Theorem for Repeated Discrete Feedback
- Steady state statistics of driven diffusions
- Directed flow in non-adiabatic stochastic pumps
- Comparison of work fluctuation relations
- Pumping-Restriction Theorem for Stochastic Networks
- The stochastic pump current and the non-adiabatic geometrical phase
- Supersymmetry and fluctuation relations for currents in closed networks
- Classical nonlinear response of a chaotic system: collective resonances
- Classical nonlinear response of a chaotic system: Langevin dynamics and spectral decomposition