A finite linear map admits an autonomous GKSL realization exactly when it is invertible and power bounded, demonstrated on a complete D2Q9 lattice Boltzmann timestep.
Carleman, Application de la theorie des equations integrales lineaires aux systemes d equations differentielles non lineaires, Acta Mathematica59, 63 (1932)
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Autonomous Lindblad Realizability of Nonunitary Linear Dynamics with a Carleman Lattice Boltzmann Application
A finite linear map admits an autonomous GKSL realization exactly when it is invertible and power bounded, demonstrated on a complete D2Q9 lattice Boltzmann timestep.