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DY: Fachverband Dynamik und Statistische Physik

DY 26: Brownian Motion, Transport and Anomalous Diffusion

DY 26.9: Vortrag

Dienstag, 17. März 2020, 12:15–12:30, HÜL 186

A finite-radius stochastic action — •Julian Kappler and Ronojoy Adhikari — Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, United Kingdom

A fundamental question associated with Langevin dynamics is to quantify the (relative) probability of individual trajectories. Due to the singular nature of an individual stochastic trajectory, quantifying its probability is both technically challenging, and the result is not directly related to any physical observable. We regularize the singular concept of an individual trajectory by considering the tubular ensemble, which consists of all stochastic trajectories that remain within a ball of small but finite radius, and with moving center given by a smooth reference path. We derive the finite-radius generalization of the Onsager-Machlup stochastic action, characterize explicitly the stochastic dynamics within the tubular ensemble, and generalize the well-known single-trajectory entropy to the tubular ensemble. Our work thus establishes the finite-radius tubular ensemble as a useful extension of a single stochastic trajectory. In particular, introducing a finite threshold distance in the discussion of path probabilities, and relating experimental observables to the Onsager-Machlup action, brings the latter within reach of direct measurement.