Perspective: How to overcome dynamical density functional theory

D. de las Heras, T. Zimmermann, F. Sammüller, S. Hermann, M. Schmidt
arXiv, 2301.12156, -, (2023)     DOI: 10.48550/arXiv.2301.12156
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We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, and machine learning nonequilibrium phenomena that occur in soft matter. To give guidance for navigating the theoretical and practical challenges that lie ahead, we discuss and exemplify the limitations of dynamical density functional theory. Instead of the implied adiabatic sequence of equilibrium states that this approach provides as a makeshift for the true time evolution, we posit that the pending theoretical tasks lie in developing a systematic understanding of the dynamical functional relationships that govern the genuine nonequilibrium physics. While static density functional theory gives a comprehensive account of the equilibrium properties of many-body systems, we argue that power functional theory is the only present contender to shed similar insights into nonequilibrium dynamics, including the recognition and implementation of exact sum rules that result from the Noether theorem. As a demonstration of the power functional point of view, we consider an idealized steady sedimentation flow of the three-dimensional Lennard-Jones fluid and machine-learn the kinematic map from the mean motion to the internal force field. This proof of concept demonstrates the significant potential of machine learning the inherent functional relationships that govern nonequilibrium many-body physics.

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