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Common Structure of Non-Hamiltonian Dynamical Theories of Macroscopic Physics

  • Miroslav Grmela
Part of the International Centre for Mechanical Sciences book series (CISM, volume 261)

Abstract

Investigation of macroscopic physical systems led to the establishment of several levels of their perception. An excellent historical account is available in Refs. 1,2. A well established level of perception consists of a class of macroscopic systems S (the elements of S are the systems that are investigated), another class of physical systems I (the elements of I are the measurement instruments) and a dynamical theory DT. A dynamical theory DT consists of the phase space H (states of systems in S are completely characterized by elements of H),a set of fundamental, also called phenomenological, quantities Q and a family of time evolution equations
(1)
f ∈ H, q ∈ Q, parametrized by q. Through the fundamental quantities q the individuality of the systems s ∈ S is expressed. The level of perception is well established if there exists an association s → q, s ∈ S, q ∈ Q such that the theoretical consequences of (1) are in good agreement with the measurements, i.e. with the results of interactions of the systems form S with the systems in I. The association S → Q represents a part of the experience, it cannot be obtained theoretically inside the chosen level.

Keywords

Local Equilibrium Dynamical Theory Common Structure Thermodynamic Equation Macroscopic System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Carnot, S., Reflection on the motive power of fire, Ed. E. Mendoza, Dover Publ., 1960.Google Scholar
  2. 2.
    Brush, S.G., Kinetic theory, vol. 1,2,3, Pergamon Press, 1966.Google Scholar
  3. 3.
    Grmela, M., Dynamic Stability and Thermodynamics in Kinetic Theory and Fluid Mechanics, J. Math. Phys. 16, 2441, 1975.ADSCrossRefMathSciNetGoogle Scholar
  4. Grmela, M. and Iscoe, I., Reductions in a Class of Dissipative Dynamical Systems of Macroscopic Physics, Ann. Inst. Henri Poincaré. XXVIII, I II, 1978.Google Scholar
  5. Grmela, M., Dissipative Dynamical Systems of Macroscopic Physics in Proceedings of the Seminar on Global Analysis, Lecture Notes in Mathematics (to appear), Eds. M. Grmela and J. Marsden, 1979.Google Scholar
  6. 4.
    Yvon, J., Les corrélations et l’entropie en mécanique statistique classique, Dunod, Paris, 1966.Google Scholar
  7. 5.
    Grmela, M., Compatibility of a Dynamical Theory with Thermodynamics, Rapport CRMA-888, 1979.Google Scholar
  8. 6.
    De Groot, S.R. and Mazur, P., Non-equilibrium thermodynamics, McGraw-Hill, New York, 1969.Google Scholar
  9. 7.
    Grmela, M. and Garcia-Colin, L.S., Compatibility of the Enskog-like Kinetic Theory with Thermodynamics Part I and II, Phys. Rev.Google Scholar
  10. 8.
    Résibois, P., H-theorem for the (modified) Non-linear Enskog Equation, J. Stat. Phys., 19, 593, 1978.ADSCrossRefGoogle Scholar
  11. 9.
    Grmela, M. and Salmon, J., in preparation.Google Scholar
  12. 10.
    Grmela, M. and Rosen, R., Some Consequences of the OnsagerCasimir Symmetry, Rapport CRMA - 753, 1979.Google Scholar

Copyright information

© Springer-Verlag Wien 1980

Authors and Affiliations

  • Miroslav Grmela
    • 1
  1. 1.Centre de recherche de mathématiques appliquéesUniversité de MontréalCanada

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