There are several approaches to the theory of continuous materials in non-equilibrium. They are the classical thermodynamics of irreversible processes, the so-called general non-linear continuum theory based on the Clausius-Duhem inequality and a recent approach which uses instead a fundamental inequality which follows from a thrifty application of the Second Law. Merits and shortcomings of these theories are discussed. It is also explained that the concept of entropy in non-equilibrium has no foundation in a consequent continuum theory; no unique entropy can be defined nor evaluated from measured dynamic and thermodynamic data. Only if other information on the atomistic structure and on the molecular mechanisms is available, may the entropy be given a meaning outside equilibrium. We would therefore assert that the concept of entropy in non-equilibrium should be completely discarded when building up a general continuum theory. Only the third of the approaches mentioned above meets this requirement.


Entropy Production Heat Bath Thermodynamic System Surface Traction Positive Matrix 
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  1. [1]
    Müller, I.: Zur Ausbreitungsgeschwindigkeit von Störungen in kontinuierlichen Medien. Aachen: 1966. ( Dissertation. )Google Scholar
  2. [2]
    Truesdell, C.: Six Lectures on Modern Natural Philosophy. Berlin—Heidelberg—New York: Springer. 1966.MATHGoogle Scholar
  3. [2a]
    Coleman, B. D., and V. J. Mizel: J. Chem. Phys. 40, 1116 (1964).MathSciNetADSCrossRefGoogle Scholar
  4. [2b]
    Truesdell, C., and W. Noll: The Non-linear Field Theories of Mechanics. Encyclopedia of Physics, Vol. III/3. Ed. S. Flügge. Berlin—HeidelbergNew York: Springer. 1965.Google Scholar
  5. [3]
    Meixner, J.: J. Appl. Mech. 1966.Google Scholar
  6. [4]
    Meixner, J.: Z. Physik 193, 366–383 (1966).ADSCrossRefGoogle Scholar
  7. [5]
    Scxottky, W.: Thermodynamik. Berlin: Springer. 1929.CrossRefGoogle Scholar
  8. [6]
    Drucker, D. C.: J. Appl. Mech. 26; Trans. ASME, Ser. E, 81, 101–106 (1959)Google Scholar
  9. Drucker, D. C. C.: “Plasticity”, Second Symposium on Naval Structural Mechanics, p. 170. Providence, R. I.: Brown Univ. 1960.Google Scholar
  10. [7]
    König, H., and J. Meixner: Math. Nachrichten 19, 265 (1958).MATHCrossRefGoogle Scholar
  11. [8]
    Meixner, J.: Arch. Ratl. Mech. Anal. 17, 278 (1964).MathSciNetMATHGoogle Scholar
  12. [9]
    Breuer, S., and E. T. Onat: J. Appl. Math. Phys. 15, 12 (1964).MathSciNetMATHGoogle Scholar
  13. [10]
    König, H., and J. Tobergte: J. reine angew. Math. 212, 104 (1963).MathSciNetMATHGoogle Scholar
  14. [11]
    Tobergte, J.: Invariante Teilräume und die verlorene Energie linearer passiver Transformationen. Köln: 1965. ( Dissertation. )Google Scholar

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© Springer-Verlag/Wien 1968

Authors and Affiliations

  • J. Meixner
    • 1
  1. 1.AachenGermany

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