Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Stochastic Thermodynamics

DY 23.5: Talk

Tuesday, April 2, 2019, 15:00–15:15, H20

Discrete delay as the limit of distributed memory – An explicit study of the limit from a thermodynamic perspective — •Sarah A. M. Loos, Simon M. Hermann, and Sabine H. L. Klapp — Institut für theoretische Physik, TU Berlin, Germany

Stochastic thermodynamics provides a consistent description of a wide class of Langevin systems [1,2], but the Markov assumption is often crucial [1,2]. While some non-Markovian systems have indeed been studied in great detail, the case of a discrete delay in a continuous control is still insufficiently understood [2,3]. This is especially true in the presence of nonlinear forces.

In this talk, I will discuss the possibility of describing delayed dynamics as the limiting case of a process with gamma-distributed memory kernel of decreasing width [4]. While the kernel indeed decays smoothly to a delta peak, generating a discrete delay, we find that the (thermo-)dynamical properties are in fact only recovered in the delta limit. We investigate a way out by introducing colored noise, which at the same time allows us to explicitly study the impact of measurement errors. In fact, we find a divergent total entropy production for the error-free case. Considering linear and nonlinear example systems, we also study work and heat [3] and their fluctuations.
[1] U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).

[2] M. L. Rosinberg, T. Munakata, G. Tarjus, PRE 91, 042114 (2015).

[3] S. A. M. Loos and S. H. L. Klapp, ArXiv:1806.04995 (2018).

[4] A. Longtin, Complex time-delay systems (Springer, 2010).