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 (1+1) 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.