Regensburg 2019 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 55: Poster: Noneq. Stat. Phys., Stat. Bio. Phys., Brownian

DY 55.9: Poster

Thursday, April 4, 2019, 15:00–18:00, Poster B2

A generalization of the thermodynamic uncertainty relation to periodically driven systems — •Timur Koyuk¹, Udo Seifert¹, and Patrick Pietzonka^1,2 — ¹II. Institut für Theoretische Physik, Universität Stuttgart, 70550 Stuttgart, Germany — ²DAMTP, Centre for Mathematical Sciences, University of Cambridge, CambridgeCB3 0WA, United Kingdom

The thermodynamic uncertainty relation expresses a universal trade-off between precision and entropy production, which applies in its original formulation to current observables in steady-state systems. We generalize this relation to periodically time-dependent systems and, relatedly, to a larger class of inherently time-dependent current observables [1]. In the context of heat engines or molecular machines, our generalization applies not only to the work performed by constant driving forces, but also to the work performed while changing energy levels. The entropic term entering the generalized uncertainty relation is the sum of local rates of entropy production, which are modified by a factor that refers to an effective time-independent probability distribution. The conventional form of the thermodynamic uncertainty relation is recovered for a time-independently driven steady state and, additionally, in the limit of fast driving. We illustrate our results for a simple model of a heat engine with two energy levels.
[1] T. Koyuk, U. Seifert, and P. Pietzonka, A generalization of the thermodynamic uncertainty relation to periodically driven systems, J. Phys. A: Math. Theor. (2018), arXiv:1809.02113, in press.