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

date: 7/15/2025, time: 16:00-17:30, room: ICS 140

Organizer: Felipe Abril-Bermúdez (University of Aberdeen)

Chair: Felipe Abril-Bermúdez (University of Aberdeen)

Multiplicative Noise and Entropy Production Rate in Stochastic Processes With Threshold

Felipe Segundo Abril Bermúdez (University of Aberdeen)

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.

Path integrals for fractional Langevin equations and anomalous phenomena

David Santiago Quevedo (Utrecht University)

In the last decades, the fractional Langevin equation has been intensively used to study anomalous diffusion and ergodicity breaking in out-of-equilibrium systems. The interplay of fractional friction kernels and random noises leads to deviations of the MSD from the usual linear behavior and the emergence of dynamical phases marked by (weak) ergodicity breaking. Notably, these include time crystals and time glasses—nontrivial regimes manifesting periodicity and metastability. In this talk, we present a generalized path integral formalism to treat multidimensional non-Markovian Langevin equations describing processes that involve fractional operators and fractional Gaussian noises. Our results recover the conventional ones for the underdamped Langevin equation and the Klein-Kramers equations, and extend them to more general settings. A general solution scheme is also presented, together with some benchmark cases.

Linking the statistics of cells in lineages and populations using Feynman-Kac.

Yaïr Hein (Utrecht)

Quantities associated with bacterial cells, such as size, growth rate, fluorescence and protein concentrations, are highly stochastic. Measurements of such quantities can either be taken from single lineage experiments or cells sampled from large exponentially growing populations. It turns out that measurements from a population sample follow slightly skewed distributions with respect to the lineage distributions. This skew is a consequence of fast-growing and fast-dividing cells being overrepresented in a growing population. In my talk, I show how one can characterize this skewed density distribution, either as an eigenfunction of a partial differential equation governing the population as a whole, or as the expected outcome of the trajectory of a single cell. The duality between these representations, both with their own real physical interpretations, is equivalent to a version of the Feynman-Kac formula. This biological problem could therefore provide an interesting intuition behind the Feynman-Kac formula itself.