Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
Abstract
A general framework for the field-theoretic thermodynamic uncertainty relation was recently proposed and illustrated with the dimensional Kardar-Parisi-Zhang equation. In the present paper, the analytical results obtained there in the weak coupling limit are tested via a direct numerical simulation of the KPZ equation with good agreement. The accuracy of the numerical results varies with the respective choice of discretization of the KPZ non-linearity. Whereas the numerical simulations strongly support the analytical predictions, an inherent limitation to the accuracy of the approximation to the total entropy production is found. In an analytical treatment of a generalized discretization of the KPZ non-linearity, the origin of this limitation is explained and shown to be an intrinsic property of the employed discretization scheme.
Keywords
Cite
@article{arxiv.2009.12126,
title = {Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation},
author = {Oliver Niggemann and Udo Seifert},
journal= {arXiv preprint arXiv:2009.12126},
year = {2021}
}