Legendre submanifolds in contact manifolds as attractors and geometric nonequilibrium thermodynamics

DOI10.1063/1.4927226zbMath1327.82072arXiv1412.5780OpenAlexW3104789338MaRDI QIDQ5500761

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Publication date: 10 August 2015

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.5780

zbMATH Keywords

Riemannian manifoldsLegendre transformcontact manifoldsHessian manifoldsLegendre submanifolds

Mathematics Subject Classification ID

Symplectic manifolds (general theory) (53D05) Global submanifolds (53C40) Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Irreversible thermodynamics, including Onsager-Machlup theory (82C35) Irreversible thermodynamics, including Onsager-Machlup theory (82B35)

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Cites Work

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• Contact structure in thermodynamic theory
• An extension of Hamiltonian systems to the thermodynamic phase space: towards a geometry of nonreversible processes
• Information geometry ofq-Gaussian densities and behaviors of solutions to related diffusion equations
• Riemannian and Finslerian geometry in thermodynamics
• Para-Sasakian geometry in thermodynamic fluctuation theory
• Liouville’s theorem and the canonical measure for nonconservative systems from contact geometry
• Hessian Structures on Deformed Exponential Families
• Information geometry in vapour–liquid equilibrium
• Structure groupU(n) × 1 in thermodynamics

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