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

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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.