Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

Morrison, Philip J.; Updike, Michael H.

doi:10.1103/PhysRevE.109.045202

Inclusive curvaturelike framework for describing dissipation: Metriplectic 4-bracket dynamics

Journal Article · Fri Apr 05 00:00:00 EDT 2024 · Physical Review E

DOI:https://doi.org/10.1103/PhysRevE.109.045202· OSTI ID:2997874

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Univ. of Texas, Austin, TX (United States)

An inclusive framework for joined Hamiltonian and dissipative dynamical systems that are thermodynamically consistent, i.e., preserve energy and produce entropy, is given. The dissipative dynamics of the framework is based on the metriplectic 4-bracket, a quantity like the Poisson bracket defined on phase space functions, but unlike the Poisson bracket has four slots with symmetries and properties motivated by Riemannian curvature. Metriplectic 4-bracket dynamics is generated using two generators, the Hamiltonian and the entropy, with the entropy being a Casimir of the Hamiltonian part of the system. The formalism includes known previous binary bracket theories for dissipation or relaxation as special cases. Rich geometrical significance of the formalism and methods for constructing metriplectic 4-brackets are explored. Many examples of both finite and infinite dimensions are given.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC)

Grant/Contract Number:: FG02-04ER54742

OSTI ID:: 2997874

Alternate ID(s):: OSTI ID: 2474584
OSTI ID: 2579600

Journal Information:: Physical Review E, Journal Name: Physical Review E Journal Issue: 4 Vol. 109; ISSN 2470-0053; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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