Niggemann, OliverSeifert, Udo2023-06-262023-06-2620200022-47151572-96131852277564http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-ds-132255http://elib.uni-stuttgart.de/handle/11682/13225http://dx.doi.org/10.18419/opus-13206We propose a field-theoretic thermodynamic uncertainty relation as an extension of the one derived so far for a Markovian dynamics on a discrete set of states and for overdamped Langevin equations. We first formulate a framework which describes quantities like current, entropy production and diffusivity in the case of a generic field theory. We will then apply this general setting to the one-dimensional Kardar-Parisi-Zhang equation, a paradigmatic example of a non-linear field-theoretic Langevin equation. In particular, we will treat the dimensionless Kardar-Parisi-Zhang equation with an effective coupling parameter measuring the strength of the non-linearity. It will be shown that a field-theoretic thermodynamic uncertainty relation holds up to second order in a perturbation expansion with respect to a small effective coupling constant. The calculations show that the field-theoretic variant of the thermodynamic uncertainty relation is not saturated for the case of the Kardar-Parisi-Zhang equation due to an excess term stemming from its non-linearity.eninfo:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/4.0/530article2023-05-15