Dresden 2026 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 9: Statistical Physics far from Thermal Equilibrium I

DY 9.4: Vortrag

Montag, 9. März 2026, 10:15–10:30, ZEU/0160

Stochastic Path Integrals for Non-Markovian Dynamics: Fractional Operators, and Entropy Production — •Felipe Abril-Bermudez — Independent Researcher (formerly University of Aberdeen, UK)

Stochastic dynamics with long-range correlations, multiplicative noise, and memory effects give rise to rich non-equilibrium behaviors, including anomalous diffusion, metastability, and nontrivial entropy production. In this work, we develop a unified stochastic path integral (SPI) framework that extends the Parisi-Sourlas supersymmetric formalism to treat multidimensional Langevin systems with multiplicative noise, thresholds, and fractional operators driven by fractional Gaussian noise. The resulting generalized Fokker-Planck equation is solved for representative processes, enabling analytical estimation of Shannon entropy and entropy production rates, which exhibit the emergence of quasi-steady states with non-monotonic dissipation. In parallel, the formalism recovers the standard underdamped Langevin and Klein-Kramers results while providing a systematic treatment of non-Markovian dynamics responsible for anomalous transport, weak ergodicity breaking, and dynamical phases such as time glasses and time crystals. Thus, it is shown how the SPI can serve as a unified approach to study anomalous stochastic phenomena in complex systems.

Keywords: Stochastic path integral; Fractional Brownian motion; Entropy production rate