A Comparison Between Power Functional Theory and Projection Operator Formalisms as Approaches to Non-Equilibrium Statistical Physics

幂泛函理论和投影算子形式是构造非热平衡系统中粗粒度观测物精确运动方程的独立方法。由于幂泛函理论是最近才引入的，目前还没有对这两种方法进行比较的研究。我们建议分析这两种方法在物理解释方面的潜力，以及它们在控制近似和数值处理方面的适用性。为了实施这个计划，我们将研究两个模型系统：一维硬棒系统和高斯核心模型。我们将用机器学习的方法来构造幂函数。

Power Functional Theory and Projection Operator Formalisms are independent approaches to construct exact equations of motion for coarse-grained observables in systems out of thermal equilibrium. As Power Functional Theory has only recently been introduced, there is no study yet, in which the two approaches are compared. We propose to ana- lyze the two approaches in terms of their potential for physical interpretation and their suitability for controlled approximation and numerical treatment. To carry out this programme, we will study two model systems: the one-dimensional hard rods system and the Gaussian core model. We will construct the power functionals by means of a machine learning approach.