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 55.6: Poster

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

Large deviations for a driven underdamped particle in a periodic potential — •Lukas P. Fischer and Udo Seifert — II. Institut für Theoretische Physik, Universität Stuttgart, Germany

Large deviation theory is a versatile tool that proved useful for establishing connections between current fluctuations and thermodynamic steady state properties, e.g. the thermodynamic uncertainty relation [1]. Previous studies, however, were limited to systems which are diffusive in all variables, i.e. overdamped Brownian motion or Markov jump processes. In a previous study we extended the work to underdamped Brownian motion of a single, driven particle in a periodic potential and derived an expression for the large deviation functional of the empirical phase space density [2]. This functional replaces the level 2.5 functional used for overdamped dynamics. Although bounds can be derived from the underdamped level 2 functional in general, a straightforward proof of the thermodynamic uncertainty relation for underdamped dynamics is not possible. In this contribution we revisit the underdamped large deviation function for a driven particle in a periodic potential with focus on the thermodynamic uncertainty relation. We present some ansatzes for thermodynamic bounds and discuss the problems arising from them. Furthermore we outline difficulties which have to be faced following other techniques.

[1] A.C. Barato, U. Seifert, Phys. Rev. Lett. 114, 158101 (2015)

[2] L.P. Fischer, P. Pietzonka, U. Seifert, Phys. Rev. E 97, 022143, (2018)