论文标题
KPZ方程的热力学不确定性关系的数值研究
Numerical Study of the Thermodynamic Uncertainty Relation for the KPZ-Equation
论文作者
论文摘要
最近提出了针对现场理论热力学不确定性关系的一般框架，并用$（1+1）$ dimensional kardar-parisi-zhang方程进行了说明。在本文中，在弱耦合极限中获得的分析结果通过以良好一致的KPZ方程的直接数值模拟进行了测试。数值结果的准确性随着KPZ非线性的离散化选择而异。尽管数值模拟强烈支持分析预测，但发现了近似值对总熵产生的准确性的固有限制。在对KPZ非线性的广义离散化的分析处理中，解释了这种限制的起源，并证明是所采用的离散化方案的内在特性。
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.
