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Noether’s theorem in statistical mechanics

Hermann, Sophie ; Schmidt, Matthias

Communications physics, 2021-08, Vol.4 (1), p.1-13, Article 176 [Periódico revisado por pares]

London: Nature Publishing Group

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Título:
Noether’s theorem in statistical mechanics
Autor: Hermann, Sophie ; Schmidt, Matthias
Assuntos: Brownian motion ; Calculus of variations ; Complex systems ; Conservation laws ; Correlation ; Correlators ; Density ; Energy conservation ; Equilibrium ; Free energy ; Hierarchies ; Identities ; Integral equations ; Integrals ; Particle spin ; Phase separation ; Sedimentation & deposition ; Statistical mechanics ; Statistical physics ; Sum rules ; Symmetry ; Theorems ; Theory of relativity ; Torque
É parte de: Communications physics, 2021-08, Vol.4 (1), p.1-13, Article 176
Descrição: Abstract Noether’s calculus of invariant variations yields exact identities from functional symmetries. The standard application to an action integral allows to identify conservation laws. Here we rather consider generating functionals, such as the free energy and the power functional, for equilibrium and driven many-body systems. Translational and rotational symmetry operations yield mechanical laws. These global identities express vanishing of total internal and total external forces and torques. We show that functional differentiation then leads to hierarchies of local sum rules that interrelate density correlators as well as static and time direct correlation functions, including memory. For anisotropic particles, orbital and spin motion become systematically coupled. The theory allows us to shed new light on the spatio-temporal coupling of correlations in complex systems. As applications we consider active Brownian particles, where the theory clarifies the role of interfacial forces in motility-induced phase separation. For active sedimentation, the center-of-mass motion is constrained by an internal Noether sum rule.
Editor: London: Nature Publishing Group
Idioma: Inglês

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Noether’s theorem in statistical mechanics

Hermann, Sophie ; Schmidt, Matthias

London: Nature Publishing Group

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