Philip Morrison
Metriplectic Geometries: Definitions and Applications
Metriplectic dynamics is a kind of dynamical system (finite or infinite) that ensures thermodynamic consistency: conservation of energy and production of entropy. It is based on the metriplectic 4-bracket that maps four phase space functions to another, and has the algebraic curvature symmetries. Metriplectic 4-brackets can be constructed using the Kulkarni-Nomizu product or via a pure Lie algebraic formalism based on the Koszul connection. The formalism produces many known and new dynamical systems. It also provides a pathway for constructing structure preserving numerical algorithms. Recent papers are below:
P. J. Morrison and M. Updike, ``Inclusive Curvature-Like Framework for Describing Dissipation: Metriplectic 4-Bracket Dynamics,” Physical Review E 109, 045202 (22pp) (2024).
A. Zaidni, P. J. Morrison, and S. Benjelloun,, ``Thermodynamically Consistent Cahn-Hilliard-Navier-Stokes Equations using the Metriplectic Dynamics Formalism,” Physica D 468, 134303 (11pp) (2024).
N. Sato and P. J. Morrison, ``A Collision Operator for Describing Dissipation in Noncanonical Phase Space,”Fundamental Plasma Physics 10, 100054 (18pp) (2024)
W. Barham, P. J. Morrison, A. Zaidni, ``A thermodynamically consistent discretization of 1D thermal-fluid models using their metriplectic 4-bracket structure," arXiv:2410.11045v2 [physics.comp-ph] 19 Oct 2024.
A. Zaidni, P. J. Morrison, ``Metriplectic 4-bracket algorithm for constructing thermodynamically consistent dynamical systems," arXiv:2501.00159v1 [physics.flu-dyn] 30 Dec 2024.
