Stochastic systems with memory

*To request access to the videoconference, email dsivak@sfu.ca

Synopsis

Real-world stochastic systems are often non-Markovian. This might be due to hydrodynamic backcoupling, viscoelastic effects, persistence in active swimmers, or an external feedback control loop acting on the system. Despite the omnipresence of memory, the theoretical understanding of non-Markovian dynamics is still in its infancy, which is especially true for systems that operate far from equilibrium. In this talk, we review the main theoretical challenges, which are connected with the acausality of the backward process, the infinite-dimensional nature of stochastic delay equations, and the non-existence of a closed Fokker-Planck descriptions [1]; and we discuss possible approaches to nevertheless treat such systems [1-3]. Focussing on thermodynamics properties, we show that feedback with time delay inevitably leads to a finite heat flow, even for vanishingly small delay [2]. We link the heat flow at small delay times to "entropy pumping", which is a phenomenon that is already established for Markovian systems subject to velocity-dependent driving, and show that delayed feedback may induce heating as well as cooling regimes [2]. We further consider systems with Gamma-distributed delay and coloured noise and calculate heat and information flows between system and environment [3]. We demonstrate that the system may be in a true nonequilibrium steady state without exchanging heat with its environment, or without exchanging information.

[1] Loos, Klapp, Jour. Stat. Phys., 177, 95–118 (2019).
[2] Loos, Klapp, Sci. Rep. 9, 2491 (2019).
[3] Loos, Hermann, Klapp, preprint: arXiv:1910.08371 (2019).