Discrete Boltzmann-like equations: a dynamical formulation

This investigation presents a dynamical formulation of Boltzmann-like discrete kinetic equations. The central concept of such a formulation is based on the idea that a dissipative system is equipped with a functional Poisson bracket and a dissipative bracket, and with two functionals generating the dynamical evolution. We present non-canonical brackets and the generating functionals. We also discuss their basic properties and investigate dynamical invariants as well as the production of entropy generated by the entropy functional via the dissipative part of the bracket. When collisions are the only sources of dissipation we are coming up with a consistent up to now unknown version of the discrete Boltzmann-Vlasov kinetic equation.