Regensburg 2019 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 23: Stochastic Thermodynamics

DY 23.6: Vortrag

Dienstag, 2. April 2019, 15:15–15:30, H20

Entropy production in systems with distributed delay via Markovian embedding — •Simon M. Hermann, Sarah A. M. Loos, and Sabine H. L. Klapp — TU Berlin

We study overdamped systems with extended memory kernels at temperature T in the framework of stochastic thermodynamics [1-3]. The (distributed) delay renders the dynamics non-Markovian. As a consequence the time-reversed process appearing in the path integral representation of the entropy production is acausal [2] making a calculation of this key quantity highly nontrivial. This can be circumvented by a Markovian embedding technique [4]. In particular, we replace the memory term by a set of n auxiliary variables with heat baths at temperature T′ coupled to the original one on a unidirectional ring. In this way, we construct a Markovian system that generates the same dynamics as the delayed system. If T′≠ 0, the additional heat baths introduce correlations in the noise. Here we consider explicitly systems with different numbers of auxiliary variables, corresponding to different memory kernels and associated noise correlations. We calculate the heat and entropy production focusing on a non-linear (bistable) system. For an infinite number of auxiliary variables the kernel collapses onto a δ-distribution producing a system with discrete delay [3].

[1] U. Seifert, Rep. Prog. Phys. 75, 126001 (2012).

[2] M. L. Rosinberg et al., PRE 91, 042114 (2015).

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

[4] F. M. Atay, ed. Complex time-delay systems. Springer, 2010.