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@ARTICLE{,
            author = {Pavelka, Michal and Klika, V. and Esen, Ogul and Grmela, Miroslav},
             title = {A hierarchy of Poisson brackets in non-equilibrium thermodynamics},
           journal = {Physica D: Nonlinear Phenomena},
            volume = {335},
              year = {2016},
             pages = {54-69},
               doi = {10.1016/j.physd.2016.06.011},
          abstract = {Reversible evolution of macroscopic and mesoscopic systems can be conveniently
constructed from two ingredients: an energy functional and a Poisson
bracket. The goal of this paper is to elucidate how the Poisson brackets can be
constructed and what additional features we also gain by the construction. In
particular, the Poisson brackets governing reversible evolution in one-particle
kinetic theory, kinetic theory of binary mixtures, binary fluid mixtures, classical
irreversible thermodynamics and classical hydrodynamics are derived from
Liouville equation. Although the construction is quite natural, a few examples
where it does not work are included (e.g. the BBGKY hierarchy). Finally, a new
infinite grand-canonical hierarchy of Poisson brackets is proposed, which leads
to Poisson brackets expressing non-local phenomena such as turbulent motion
or evolution of polymeric fluids. Eventually, Lie-Poisson structures standing
behind some of the brackets are identified.},
  Preprint project = {NCMM},
     Preprint year = {2016},
   Preprint number = {22},
       Preprint ID = {NCMM/2016/22}
}