Metriplectic systems converge to entropy extrema at fixed Hamiltonian under stated conditions; a Landau-inspired class reduces the check to two simpler conditions for use in equilibrium relaxation schemes.
Materassi, Metriplectic algebra for dissipative fluids in Lagrangian formulation, Entropy 17 (3) (2015) 1329–1346
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Metriplectic relaxation to equilibria
Metriplectic systems converge to entropy extrema at fixed Hamiltonian under stated conditions; a Landau-inspired class reduces the check to two simpler conditions for use in equilibrium relaxation schemes.