CS48: Path Integral Formalism for Stochastic Processes: Applications in Physics and Biology

Organizer: Felipe Abril-Bermúdez (University of Aberdeen)

Multiplicative Noise and Entropy Production Rate in Stochastic Processes With Threshold

Felipe Segundo Abril Bermúdez

The stochastic path integral formalism (SPI) provides a powerful framework that generalizes the path integral approach from quantum mechanics to stochastic processes, enabling the study of systems governed by randomness and noise. Leveraging the Parisi-Sourlas supersymmetric formalism for Langevin equations, this framework extends traditional stochastic differential equations (SDEs) to encompass systems with multiplicative noise and long-range correlations (arbitrary noises). A generalized Fokker-Planck equation is derived and solved for two stochastic processes with thresholds, enabling the estimation of Shannon entropy and entropy production rates. The results reveal the emergence of quasi-steady states characterized by a non-monotonic behavior in the entropy production rate.