WIAS Preprint No. 2733, (2020)

Multiscale thermodynamics of charged mixtures


  • Vágner, Petr
    ORCID: 0000-0001-5952-0025
  • Pavelka, Michal
  • Esen, Oğul
    ORCID: 0000-0002-6766-0287

2010 Mathematics Subject Classification

  • 78A25 35Q61 82B35


  • GENERIC, electrodynamics, continuum mechanics, non-equilibrium thermodynamics, polarization, magnetization, multiscale modeling, hamiltonian mechanics




A multiscale theory of interacting continuum mechanics and thermodynamics of mixtures of fluids, electrodynamics, polarization and magnetization is proposed. The mechanical (reversible) part of the theory is constructed in a purely geometric way by means of semidirect products. This leads to a complex Hamiltonian system with a new Poisson bracket, which can be used in principle with any energy functional. The thermodynamic (irreversible) part is added as gradient dynamics, generated by derivatives of a dissipation potential, which makes the theory part of the GENERIC framework. Subsequently, Dynamic MaxEnt reductions are carried out, which lead to reduced GENERIC models for smaller sets of state variables. Eventually, standard engineering models are recovered as the low-level limits of the detailed theory. The theory is then compared to recent literature.

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