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Symplectic Foliation Structures of Non-Equilibrium Thermodynamics as Dissipation Model: Application to Metriplectic Nonlinear Lindblad Quantum Master Equation [PDF]

Entropy, 2022
The idea of a canonical ensemble from Gibbs has been extended by Jean-Marie Souriau for a symplectic manifold where a Lie group has a Hamiltonian action.
Frédéric Barbaresco
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Jean-Marie Souriau’s Symplectic Foliation Model of Sadi Carnot’s Thermodynamics [PDF]

Entropy
The explanation of thermodynamics through geometric models was initiated by seminal figures such as Carnot, Gibbs, Duhem, Reeb, and Carathéodory. Only recently, however, has the symplectic foliation model, introduced within the domain of geometric ...
Frédéric Barbaresco
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Global Geometry of Bayesian Statistics [PDF]

Entropy, 2020
In the previous work of the author, a non-trivial symmetry of the relative entropy in the information geometry of normal distributions was discovered. The same symmetry also appears in the symplectic/contact geometry of Hilbert modular cusps. Further, it
Atsuhide Mori
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Derived brackets in bosonic string sigma-model

Nuclear Physics B, 2022
We study the worldsheet theory of bosonic string from the point of view of the BV formalism. We explicitly describe the derived Poisson structure which arises when we expand the Master Action near a Lagrangian submanifold.
Vinícius Bernardes, Andrei Mikhailov, Eggon Viana   +2 more
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Leaves of stacky Lie algebroids

Comptes Rendus. Mathématique, 2020
We show that the leaves of an LA-groupoid which pass through the unit manifold are, modulo a connectedness issue, Lie groupoids. We illustrate this phenomenon by considering the cotangent Lie algebroids of Poisson groupoids thus obtaining an interesting ...
Álvarez, Daniel
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Asymptotic dynamics of three dimensional supergravity and higher spin gravity revisited

Journal of High Energy Physics, 2023
We reconsider the Hamiltonian reduction of the action for three dimensional AdS supergravity and W 3 higher spin AdS gravity in the Chern-Simons formulation under asymptotically anti-de Sitter boundary conditions.
Wout Merbis, Turmoli Neogi, Arash Ranjbar   +2 more
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The Higgs mechanism — Hasse diagrams for symplectic singularities

Journal of High Energy Physics, 2020
We explore the geometrical structure of Higgs branches of quantum field theories with 8 supercharges in 3, 4, 5 and 6 dimensions. They are symplectic singularities, and as such admit a decomposition (or foliation ) into so-called symplectic leaves, which
Antoine Bourget, Santiago Cabrera, Julius F. Grimminger, Amihay Hanany, Marcus Sperling, Anton Zajac, Zhenghao Zhong   +6 more
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Geometric Models for Lie–Hamilton Systems on ℝ²

Mathematics, 2019
This paper provides a geometric description for Lie−Hamilton systems on R 2 with locally transitive Vessiot−Guldberg Lie algebras through two types of geometric models. The first one is the restriction of a class of Lie−Hamilton
Julia Lange, Javier de Lucas
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Singularities in Calogero–Moser varieties

Forum of Mathematics, Sigma
In this article, we describe completely the singularities appearing in Calogero–Moser varieties associated (at any parameter) to the wreath product symplectic reflection groups.
Gwyn Bellamy, Ruslan Maksimau, Travis Schedler   +2 more
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Geometric Structures on Spaces of Weighted Submanifolds

Symmetry, Integrability and Geometry: Methods and Applications, 2009
In this paper we use a diffeo-geometric framework based on manifolds that are locally modeled on ''convenient'' vector spaces to study the geometry of some infinite dimensional spaces.
Brian Lee
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