Berlin 2018 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 43: Stochastic thermodynamics and information processing

DY 43.11: Talk

Wednesday, March 14, 2018, 12:45–13:00, BH-N 243

Towards a (stochastic) thermodynamic description of non-Markovian delayed systems — •Sarah A. M. Loos and Sabine H. L. Klapp — Institut für Theoretische Physik, TU Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany

Stochastic thermodynamics provides a consistent description of a wide class of Langevin systems, but the Markov assumption is often crucial [1]. However, time-delayed feedback control – which commonly arises for example in biological processes and technical applications – renders stochastic dynamics non-Markovian [2]. Therefore, some basic concepts need to be revisited [3]. Time-delay further pushes the steady states out of thermodynamic equilibrium (even in the absence of probability currents), as reflected by a non-zero mean entropy production. This is explicitly shown in [4] for the case of linear forces and an exponential memory kernel in one dimension.

Here, we discuss the possibility of calculating key thermodynamic quantities in the steady state of overdamped Langevin systems involving different memory kernels and nonlinear external forces. Using a Markovian embedding, we find a divergent entropy production in the case of error-free and continuous measurement. Furthermore, we present an analytical expression for the heat exchange rates that only involves positional moments.

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

[2] S. A. M. Loos and S. H. L. Klapp, PRE 96, 012106 (2017).

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

[4] A. Crisanti, A. Puglisi, D. Villamaina, PRE 85, 061127 (2012).