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)


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
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.


Local Equilibrium Dynamical Theory Common Structure Thermodynamic Equation Macroscopic System 
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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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