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.

最近提出了场理论热力学不确定性关系的通用框架，并用\（（1 + 1）\）进行了说明。维Kardar–Parisi–Zhang方程。在本文中，通过对KPZ方程的直接数值模拟并取得了良好的一致性，测试了在弱耦合极限条件下获得的分析结果。数值结果的准确性随KPZ非线性离散化的相应选择而变化。数值模拟强有力地支持了分析预测，但发现了对总熵产生近似值的准确性的内在限制。在对KPZ非线性的广义离散化的分析处理中，解释了此限制的根源，并将其显示为所采用离散化方案的固有属性。