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.
Brockett, Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra and its Applications 146 (1991) 79–91
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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.