Dissipative brackets as a tool for kinetic modeling

A generalization of the previously introduced dissipative bracket formulation of dissipative kinetic equations is performed. This generalization offers an opportunity to write model equations in concordance with the entropy requirements in situations where one attempts to consider the dissipative dynamics near highly non-equilibrium states. A list of sufficient conditions generalizing both the detailed balance and the Stueckelberg unitarity condition is established for the relevant kinetic equations to have an analog of the Boltzmann H-theorem. Several specific patterns of an explicit derivation of the model kinetic equations are discussed, including the relaxation in a given initial direction, the relaxation between two non-equilibrium states, and the slow decay to the equilibrium.