In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.
Microscopic derivation of the thin film equation using the Mori-Zwanzig formalism
DAMTP, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）；Institute of Physical Chemistry, Universität Münster（明斯特大学物理化学研究所）；Institute of Theoretical Physics, Center for Soft Nanoscience, Universität Münster（明斯特大学理论物理学院软纳米科学中心）
Extended dynamical density functional theory for nonisothermal binary systems including momentum density
Johannes Gutenberg-Universität Mainz（美因茨约翰内斯·古腾堡大学）；Heinrich-Heine-Universität Düsseldorf（杜塞尔多夫海因里希·海涅大学）；University of Bayreuth（拜罗伊特大学）；RWTH Aachen University（亚琛工业大学）；DWI – Leibniz Institute for Interactive Materials（莱布尼兹交互材料研究所）；University of Münster（明斯特大学）
