# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 32: Focus Session: Physics of Fluctuating Paths (joint session DY/CPP)

### DY 32.11: Vortrag

### Mittwoch, 29. März 2023, 17:45–18:00, ZEU 160

**Sojourn probabilities for diffusive dynamics with state-dependent friction: Theory and experiment** — Alice Thorneywork^{1, 2}, Jannes Gladrow^{2, 3}, Ulrich F. Keyser^{2}, Ronojoy Adhikari^{4}, and •Julian Kappler^{4, 5} — ^{1}Department of Chemistry, University of Oxford, Oxford, United Kingdom — ^{2}Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom — ^{3}Microsoft Research, Cambridge, United Kingdom — ^{4}Department of Applied Mathematics and Theoretical Physics, Cambridge University, Cambridge, United Kingdom — ^{5}Fakultät für Physik, Ludwig-Maximilians-Universität, München, Germany

The trajectories of diffusion processes are continuous but nondifferentiable, and each occurs with vanishing probability. This introduces a gap between theory, where path probabilities are used in many contexts, and experiment, where only events with nonzero probability are measurable. We bridge this gap by considering the sojourn probability, i.e. the probability for diffusive trajectories to remain within a tube of small but finite radius around a smooth path. For systems with state-dependent diffusivity, we show that the sojourn probability is characterized by a functional that is different from all previously reported multiplicative-noise stochastic actions. We corroborate our theoretical results by comparison to experimentally measured sojourn probabilities for a colloidal particle in a corrugated microchannel. Our work directly connects the discussion of path probabilities for diffusive dynamics with state-dependent friction to physical observables.