Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

DY: Fachverband Dynamik und Statistische Physik

DY 37: Brownian Motion and Anomalous Diffusion

DY 37.1: Vortrag

Donnerstag, 20. März 2025, 15:00–15:15, H43

A universal class of exactly solvable diffusions — •Costantino Di Bello¹, Edgar Roldan², and Ralf Metzler¹ — ¹Potsdam University, Institute of Physics and Astronomy, Potsdam-Golm, Germany — ²ICTP, Quantitative Life Sciences section, Trieste, Italy

We consider a general one-dimensional overdamped diffusion model described by the Ito stochastic differential equation (SDE) dX_t = µ(X_t,t) dt + σ(X_t,t) dW_t, where W_t is the standard Wiener process. We obtain a specific condition that µ and σ must fulfill in order to be possible to solve the SDE via mapping the generic process, using a suitable space-time transformation, into the simpler Wiener process. By taking advantage of this transformation, we obtain the propagator in the case of open, reflecting, and absorbing boundary conditions for a large class of diffusion processes. With the same technique, we were also able to derive the first passage time (FPT) statistics of a large class of models. Moreover, as many physical observables in stochastic thermodynamics are described by an SDE of the same form, our result can provide the analytical expression of the probability distribution of many observables like work, entropy et similia. We stress the fact that our results are valid for many non-autonomous, non-linear and non-homogeneous processes.

Keywords: Stochastic differential equations; Stochastic processes; First passage time; Stochastic thermodynamics