Equilibrium Spacetime Correlations of the Toda Lattice on the Hydrodynamic Scale

Mazzuca, Guido; Грава, Тамара; Kriecherbauer, Thomas; McLaughlin, Kenneth T-R; Mendl, Christian B.; Spohn, Herbert

doi:10.48550/arxiv.2301.02431

Cited by 1 publication

(1 citation statement)

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“…While we have restricted ourselves to discussing the point of view of functional relationships, it would be interesting to explore in future work possible cross connections to other theoretical approaches, such as Onsager's variational principle for soft matter [128][129][130][131], stochastic thermodynamics [132], large deviation theory [133,134], mode-coupling theory [135,136], generalized hydrodynamics [137], local molecular field theory for nonequilibrium systems [138], as well as to the physics of nonequilibrium phase transitions [139], Brownian solitons [140], and crystal dynamics [141][142][143][144] and non-isothermal situations [145]. Implications of the machine-learning methodology are summarized at the end of the appendix.…”

Section: Discussionmentioning

confidence: 99%

Perspective: How to overcome dynamical density functional theory

Heras

Zimmermann

Sammüller

et al. 2023

J. Phys.: Condens. Matter

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We argue in favour of developing a comprehensive dynamical theory for rationalizing, predicting, designing, 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. The trained model is capable of both predicting and designing the steady state dynamics universally for various target density modulations. This demonstrates the significant potential of using such techniques in nonequilibrium many-body physics and overcomes both the conceptual constraints of dynamical density functional theory as well as the limited availability of its analytical functional approximations.

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