Dirac structures in nonequilibrium thermodynamics

François Gay-Balmaz*, Hiroaki Yoshimura

*この研究の対応する著者

研究成果: Article査読

13 被引用数 (Scopus)

抄録

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution equations for nonequilibrium thermodynamics admit an intrinsic formulation in terms of Dirac structures, both on the Lagrangian and the Hamiltonian settings. In the absence of irreversible processes, these Dirac structures reduce to canonical Dirac structures associated with canonical symplectic forms on phase spaces. Our geometric formulation of nonequilibrium thermodynamic thus consistently extends the geometric formulation of mechanics, to which it reduces in the absence of irreversible processes. The Dirac structures are associated with the variational formulation of nonequilibrium thermodynamics developed in the work of Gay-Balmaz and Yoshimura, J. Geom. Phys. 111, 169-193 (2017a) and are induced from a nonlinear nonholonomic constraint given by the expression of the entropy production of the system.

本文言語English
論文番号012701
ジャーナルJournal of Mathematical Physics
59
1
DOI
出版ステータスPublished - 2018 1月 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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