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Thermodynamics based on the Hahn-Banach Theorem: The Clausius inequality

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References

  1. Bourbaki, N., General Topology, Parts 1 and 2, Paris: Hermann, 1966. (All page numbers cited refer to Part 1 unless otherwise specified.)

    Google Scholar 

  2. Choquet, G., Lectures on Analysis, Vols. I–III, (eds. J. Marsden, T. Lance and S. Gelbart) New York: W. A. Benjamin Inc., 1969.

    Google Scholar 

  3. Coleman, B. D., Thermodynamics of materials with memory, Arch. Rational Mech. Anal., 17, 1 (1964).

    Google Scholar 

  4. Coleman, B. D., & W. Noll, The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rational Mech. Anal., 13, 167 (1963).

    MATH  Google Scholar 

  5. Coleman, B. D., & D. R. Owen, A mathematical foundation for thermodynamics, Arch. Rational Mech. Anal., 54, 1 (1974).

    Google Scholar 

  6. Coleman, B. D., D. R. Owen & J. B. Serrin, The second law of thermodynamics for systems with approximate cycles, Arch. Rational Mech. Anal., 77, 103 (1981).

    Google Scholar 

  7. Day, W. A., Thermodynamics based on a work axiom, Arch. Rational Mech. Anal., 31, 1 (1968).

    Google Scholar 

  8. Denbigh, K., The Principles of Chemical Equilibrium, 3rd ed., Cambridge University Press, Cambridge, 1971.

    Google Scholar 

  9. Debreu, F., Representation of a preference ordering by a numerical function, pp. 159–165 of Decision Processes, eds. R. M. Thrall, C. H. Coombs and R. L. Davis, Wiley, New York, 1954.

    Google Scholar 

  10. Dieudonné, J., Foundations of Modern Analysis, Academic Press, New York, 1969.

    Google Scholar 

  11. Feynman, R., The Character of Physical Law. Cambridge, Mass.: MIT Press, 1965.

    Google Scholar 

  12. Feinberg, M., & R. Lavine, Preliminary notes on the second law of thermodynamics, July 2, 1978.

  13. Fosdick, R. L., & J. Serrin, Global properties of continuum thermodynamic processes. Arch. Rational Mech. Anal., 59, 97 (1975).

    Google Scholar 

  14. Gibbs, J. W., On the equilibrium of heterogeneous substances [Trans. Conn. Acad., 3, 108–248, 343–524 (1875–1878)]. The Scientific Papers of J. Willard Gibbs, Vol. 1, 55–353. New York: Dover Publications, 1961.

    Google Scholar 

  15. Gurtin, M. E., & W. O. Williams, An axiomatic foundation for continuum thermodynamics. Arch. Rational Mech. Anal., 26, 83 (1967).

    Google Scholar 

  16. Kelley, J. L., General Topology. New York: D. Van Nostrand, 1955.

    Google Scholar 

  17. Kelley, J. L., & I. Namioka, Linear Topological Spaces. Berlin Heidelberg New York: Springer 1963.

    Google Scholar 

  18. Noll, W., Lectures on the foundations of continuum mechanics and thermodynamics. Arch. Rational Mech. Anal., 52, 62 (1973).

    Google Scholar 

  19. Noll, W., On certain convex sets of measures and on phases of reacting mixtures. Arch. Rational Mech. Anal., 38, 1 (1970).

    Google Scholar 

  20. Owen David, R., The second law of thermodynamics for semi-systems with few approximate cycles, Arch. Rational Mech. Anal., 80, 39 (1982).

    Google Scholar 

  21. Pitteri, M., Classical thermodynamics of homogeneous systems based upon Carnot's general axiom, Arch. Rational Mech. Anal., 80, 333 (1982).

    Google Scholar 

  22. Rudin, W., Real and Complex Analysis, 2nd ed. New York: McGraw-Hill, 1974.

    Google Scholar 

  23. Rudin, W., Functional Analysis. New York: McGraw-Hill, 1973.

    Google Scholar 

  24. Serrin, J., The concepts of thermodynamics, in Contemporary Developments in Continuum Mechanics and Partial Differential Equations (eds. G. de la Penha and L. A. J. Medeiros). Amsterdam: North-Holland Publishing Co. 1978.

    Google Scholar 

  25. Serrin, J., Conceptual analysis of the classical second laws of thermodynamics. Arch. Rational Mech. Anal., 70, 355 (1979).

    Google Scholar 

  26. Serrin, J., Mathematical Foundations of Thermodynamics, notes of lectures delivered at the University of Naples, summer, 1980.

  27. Šilhavý, M., On measures, convex cones, and foundations of thermodynamics I. Systems with vector-valued actions, II. Thermodynamic systems, Czechoslovak Journal of Physics, B 30, 841–861 and 961–991 (1980).

    Google Scholar 

  28. Truesdell, C., The Tragicomical History of Thermodynamics 1822–1854. Berlin Heidelberg New York: Springer 1980.

    Google Scholar 

  29. Truesdell, C., Absolute temperatures as a consequence of Carnot's general axiom. Arch. History of Exact Sciences, 20, 357 (1979).

    Google Scholar 

  30. Truesdell, C., Rational Thermodynamics, 2nd ed., in press.

  31. Truesdell, C., & S. Bharatha, The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines. Berlin Heidelberg New York: Springer 1977.

    Google Scholar 

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Authors and Affiliations

  1. Department of Chemical Engineering, University of Rochester, Rochester, New York

    M. Feinberg & R. Lavine

  2. Department of Mathematics, University of Rochester, Rochester, New York

    M. Feinberg & R. Lavine

Authors
  1. M. Feinberg
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  2. R. Lavine
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Feinberg, M., Lavine, R. Thermodynamics based on the Hahn-Banach Theorem: The Clausius inequality. Arch. Rational Mech. Anal. 82, 203–293 (1983). https://doi.org/10.1007/BF00261935

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