Dirac structures in nonequilibrium thermodynamics

DOI10.1063/1.5017223zbMath1383.82043arXiv1704.03935OpenAlexW3102168620MaRDI QIDQ3134132

Hiroaki Yoshimura, François Gay-Balmaz

Publication date: 8 February 2018

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

Full work available at URL: https://arxiv.org/abs/1704.03935

zbMATH Keywords

Dirac structuresnonequilibrium thermodynamics

Mathematics Subject Classification ID

Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Nonholonomic systems related to the dynamics of a system of particles (70F25) Irreversible thermodynamics, including Onsager-Machlup theory (82C35) Variational principles of physics (49S05) Nonholonomic dynamical systems (37J60)

Related Items (9)

Control of port-Hamiltonian differential-algebraic systems and applications ⋮ Infinite dimensional Lagrange-Dirac mechanics with boundary conditions ⋮ Dirac structures in nonequilibrium thermodynamics for simple open systems ⋮ From variational to bracket formulations in nonequilibrium thermodynamics of simple systems ⋮ Elementary thermo-mechanical systems and higher order constraints ⋮ A free energy Lagrangian variational formulation of the Navier–Stokes–Fourier system ⋮ Stochastic port-Hamiltonian systems ⋮ Dirac Structures and Variational Formulation of Thermodynamics for Open Systems ⋮ Hamiltonian classical thermodynamics and chemical kinetics

Cites Work

• A Lagrangian variational formulation for nonequilibrium thermodynamics. I: Discrete systems.
• A Lagrangian variational formulation for nonequilibrium thermodynamics. II: Continuum systems.
• Dirac structures in Lagrangian mechanics. I: Implicit Lagrangian systems
• Dirac structures in Lagrangian mechanics. II: Variational structures
• Contact structure in thermodynamic theory
• Various approaches to conservative and nonconservative nonholonomic systems
• Nonholonomic mechanics and control. With the collaboration of J. Baillieul, P. Crouch, and J. Marsden. With scientific input from P. S. Krishnaprasad, R. M. Murray, and D. Zenkov.
• To the piston problem
• An extension of Hamiltonian systems to the thermodynamic phase space: towards a geometry of nonreversible processes
• A simple piston problem in one dimension
• Lagrangian systems with higher order constraints
• Variational discretization of the nonequilibrium thermodynamics of simple systems
• Dirac Manifolds
• Thermodynamics of systems with internal adiabatic constraints: time evolution of the adiabatic piston
• A generalization of Chetaev’s principle for a class of higher order nonholonomic constraints
• A free energy Lagrangian variational formulation of the Navier–Stokes–Fourier system
• Generalized Hamiltonian Dynamics
• Dynamics of a heavy particle surrounded by a finite number of light particles
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