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Thermodynamics and geometry

MAR 01, 1976
In the fulfillment of a goal envisioned by Gibbs, the laws of thermodynamics have been written in the form of a Euclidian metric geometry; its formulas can be read off from simple diagrams.
Frank Weinhold

It is perhaps appropriate that, in a year marking the 100th anniversary of his landmark paper in thermodynamics, new developments should call fresh attention to the special beauty and profundity of the work of J. Willard Gibbs. Recent work has proved the possibility of constructing a new representation of equilibrium thermodynamics, one that is couched in a mathematical language—an intrinsically geometrical structure—quite different from that generally employed.

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References

  1. 1. F. Weinhold, J. Chem. Phys. 63, 2479, 24842488, 2496 (1975); https://doi.org/JCPSA6
    F. Weinhold, 65 (1976) (to be published).https://doi.org/JCPSA6 , J. Chem. Phys.

  2. 2. H. B. Callen, Thermodynamics, John Wiley, New York (1960), page 48.

  3. 3. J. W. Gibbs, Trans. Conn. Acad. Arts Sci. 2, 309, 382 (1873); https://doi.org/TCAAAL
    The Collected Works of J. Willard Gibbs, Longmans, Green, New York (1928);
    Dover, New York (1961); volume I, pages 1, 33.

  4. 4. P. Dennery, A. Krzywicki, Mathematics for Physicists, Harper and Row, New York (1967), page 109.

  5. 5. C. Carathéodory, Math. Ann. 67, 355 (1909).https://doi.org/MAANA3

  6. 6. J. W. Gibbs, Elementary Principles of Statistical Mechanics, Dover, New York (1960), preface.

  7. 7. J. von Neumann, Mathematical Foundations of Quantum Mechanics, Princeton U.P., Princeton, N.J. (1955).

More about the authors

Frank Weinhold, Stanford University.

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This Content Appeared In
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Volume 29, Number 3

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