A new metriplectic system on contact manifolds is introduced for thermodynamic consistency.
problem Developing a thermodynamically consistent dynamical system on contact manifolds.
method Introducing a metriplectic dynamical system on the one-jet bundle J1N. result The metriplectic system is thermodynamically consistent, with H˙=0 and S˙≥0. A new framework describes dissipation using a metriplectic 4-bracket.
problem Describing dissipation in a way that preserves energy and entropy.
method Using a metriplectic 4-bracket, a quantity like the Poisson bracket with symmetries motivated by Riemannian curvature.
result The metriplectic 4-bracket dynamics includes all known previous binary bracket theories for dissipation.
In this paper we study the differential systems on Leibniz algebroids. We introduce a class of almost metriplectic manifolds as a special case of Leibniz manifolds. Also, the notion of almost metriplectic algebroid is introduced. These types of algebroids are used in the presentation of associated differential systems.…
Develops neural networks for learning physics of complex systems by enforcing thermodynamics principles.
problem Learning physics of complex systems from incomplete experimental data.
method Integrates port-metriplectic formalism with neural networks to enforce thermodynamics principles.
result Neural networks can learn physics of complex systems by parts, reducing learning burden.
Geometrically reformulates GENERIC stochastic dynamics.
problem Unified treatment of reversible and dissipative dynamics.
method Introduces degenerate Poisson structure, co-metric, and volume form.
result Preserves Boltzmann measure, conserves energy, reduces to deterministic limit.
The paper integrates dissipative and curl forces using geometric methods.
problem Incorporating dissipative forces into curl forces for non-conservative systems.
method Geometric metriplectic approach, Herglotz principle, generalized Euler-Lagrange equation, Galley's method.
result Natural formulations for Lagrangian and Hamiltonian dynamics of non-conservative systems.
In this note we discuss conditions under which a linear connection on a manifold equipped with both a symmetric (Riemannian) and a skew-symmetric (almost-symplectic or Poisson) tensor field will preserve both structures.
Develops neural networks that follow thermodynamics principles.
problem Learning physical systems from data while respecting thermodynamics.
method Uses feedforward neural networks and the GENERIC formalism to enforce metriplectic structure.
result Predictions comply with first and second principles of thermodynamics.
Algorithm learns latent variables for thermodynamically-consistent deep neural networks.
problem Predicting time evolution of large-scale physical systems with thermodynamic consistency.
method Sparse autoencoders and structure-preserving neural networks.
result Method conserves total energy and entropy inequality for both conservative and dissipative systems.
Framework preserves emergent physics in non-equilibrium systems from particle trajectories.
problem Linking short spatiotemporal scales to emergent bulk physics in multiscale systems.
method Metriplectic bracket formalism for structure-preserving coarse-graining.
result Preservation of thermodynamic laws and conservation in machine-learned dynamics.
Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints. We define Leibniz-Dirac structures which lead to a natural generalization of Dira…
Derives equations for interacting Lie-Poisson systems using 2-cocycle extensions.
problem Understanding collective motion of interacting Lie-Poisson systems.
method Derives equations on dual space of extended structure, including 2-cocycle terms.
result Provides most general realization of Lie-Poisson system coupling.
Geometric derivation of quantum dynamics from Lie group actions.
problem Deriving quantum dynamics from geometric principles.
method Euler-Poincaré reduction on adjoint-coupled semidirect products.
result Reproduces the Lindblad equation from geometric reduction.