6 papers
Dirac structures on tangent bundles: a geometric framework for variational principles, constrained dynamics, and symmetry reduction
Hiroaki Yoshimura
We introduce a Dirac structure on the tangent bundle of a configuration manifold, called a \textit{Lagrange--Dirac structure}, which is naturally induced by the Lagrangian two-form…
A variational formulation of stochastic thermodynamics: Spatially extended systems
Héctor Vaquero del Pino, François Gay-Balmaz, Hiroaki Yoshimura +1
Stochastic field theories are often constructed phenomenologically, without a systematic assessment of thermodynamic consistency or local detailed balance. This may hinder a physic…
Variational formulation of stochastic thermodynamics: Finite-dimensional systems
Héctor Vaquero del Pino, François Gay-Balmaz, Hiroaki Yoshimura +1
In this paper, we develop a variational foundation for stochastic thermodynamics of finite-dimensional, continuous-time systems. Requiring the second law (non-negative average tota…
Infinite-dimensional Lagrange-Dirac systems with boundary energy flow I: Foundations
François Gay-Balmaz, Ãlvaro RodrÃguez Abella, Hiroaki Yoshimura
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a l…
Infinite-dimensional Lagrange-Dirac systems with boundary energy flow II: Field theories with bundle-valued forms
François Gay-Balmaz, Ãlvaro RodrÃguez Abella, Hiroaki Yoshimura
Part I of this paper introduced the infinite dimensional Lagrange-Dirac theory for physical systems on the space of differential forms over a smooth manifold with boundary. This ap…
Discrete Dirac structures and discrete Lagrange--Dirac dynamical systems in mechanics
Linyu Peng, Hiroaki Yoshimura
In this paper, we propose the concept of -discrete Dirac structures over a manifold, where we define -discrete two-forms on the manifold and incorporate discrete cons…