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

功率泛函理论和投影算子形式是独立的方法来构造精确的运动方程的粗粒度的可观的系统的热平衡。由于功率泛函理论是最近才被引入的，因此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的物理解释的潜力和控制近似和数值处理的适用性。为了实现这一计划，我们将研究两个模型系统：一维硬棒系统和高斯核模型。我们将通过机器学习方法来构造幂泛函。

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.