Skip to main content
Log in

A Riemannian geometry for thermodynamic state space

  • Papers
  • Published:
Czechoslovak Journal of Physics Aims and scope

Abstract

We consider a class of thermodynamic systems in which the dynamics of the spontaneous approach to equilibrium is governed by the gradient of negentropy, where the gradient is taken with respect to a Riemannian metric. In open systems (dissipative structures) this gradient field is superposed with a vector field of interactions with environment. We consider three characteristics of the “economy” of dissipative structures: negentropy inflow (income), negentropy consumption (i.e. entropy production), and negentropy surplus (reserves). We derive explicit formulas for these characteristics and for the relations between them.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Akin E.: The Geometry of Population Genetics. Lecture Notes in Biomathematics 31. Springer-Verlag, Berlin, 1979.

    Google Scholar 

  2. Callen H. B.: Thermodynamics. John Wiley & Sons, New York, 1960.

    Google Scholar 

  3. Horn F., Jackson, R.: Arch. Ration. Mech. Anal.47 (1972) 81.

    Google Scholar 

  4. Nicolis G., Prigogine, I.: Self-Organization in Nonequilibrium Systems. From Dissipative Systems to Order through Fluctuations. J. Wiley & Sons, New York, 1977.

    Google Scholar 

  5. Roberts A. W., Varberg, D. E.: Convex Functions. Academic Press, New York, 1973.

    Google Scholar 

  6. Rockafellar R. Tyrell: Convex Analysis. Princeton University Press, Princeton, 1970.

    Google Scholar 

  7. Schrödinger E.: What is Life? Cambridge University Press, London, 1944.

    Google Scholar 

  8. Šilhavý M.: Czech. J. Phys. B30 (1980) 841; 961.

    Google Scholar 

  9. Straumann N.: Thermodynamik. Springer-Verlag, Berlin, 1986.

    Google Scholar 

  10. Truesdell, C.: Rational Thermodynamics. Springer-Verlag, Berlin, 1984.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kůrka, P. A Riemannian geometry for thermodynamic state space. Czech J Phys 42, 849–859 (1992). https://doi.org/10.1007/BF01605163

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01605163

Keywords

Navigation