Microcanonical phase transitions for the vortex system

DOI10.2140/memocs.2024.12.85zbMath1530.35309arXiv2307.00345MaRDI QIDQ6192398

Emanuele Caglioti, Margherita Nolasco, Dario Benedetto

Publication date: 12 February 2024

Published in: Mathematics and Mechanics of Complex Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2307.00345

zbMATH Keywords

phase transitionsmicrocanonical ensemblemean-field equationvortex system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Phase transitions (general) in equilibrium statistical mechanics (82B26) PDEs in connection with statistical mechanics (35Q82) Variational methods applied to problems in statistical mechanics (82M30)

Cites Work

• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description
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• Negative-temperature states and large-scale, long-lived vortices in two-dimensional turbulence
• The micro-canonical point vortex ensemble: Beyond equivalence
• Global bifurcation analysis of mean field equations and the Onsager microcanonical description of two-dimensional turbulence
• Non-degeneracy, mean field equations and the Onsager theory of 2D turbulence
• A special class of stationary flows for two-dimensional Euler equations: A statistical mechanics description. II
• Existence and uniqueness for mean field equations on multiply connected domains at the critical parameter
• Supercritical mean field equations on convex domains and the Onsager's statistical description of two-dimensional turbulence
• Statistical mechanics of two-dimensional vortices in a bounded container
• Statistical mechanics of classical particles with logarithmic interactions
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