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Zeitschrift für Physik B Condensed Matter

, Volume 59, Issue 4, pp 449–454 | Cite as

Thermodynamic metric and stochastic measures

  • F. Schlögl
Article

Abstract

A modification of the thermodynamic Weinhold metric is introduced by the statistical scheme of bit-number cumulants discussed in earlier papers. It is a metric in the space of intensive thermal variables and becomes identical with the Weinhold metric if transformed into the space of extensive variables. The quadratic forms of the metric tensor are different for finite distances. The here presented metric is signified by quantities defined in general statistics, distinguished by important invariance properties and moreover it brings simplifications.

Keywords

Spectroscopy Neural Network State Physics Complex System General Statistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Weinhold, F.: J. Chem. Phys.63, 2479 (1975);63, 2482 (1975);63, 2488 (1975);63, 2496 (1975);65, 559 (1976)Google Scholar
  2. 2.
    Salamon, P., Andresen, B., Gait, P.D., Berry, R.S.: J. Chem. Phys.73, 1001 (1980)Google Scholar
  3. 3.
    Salamon, P., Berry, R.S.: Phys. Rev. Lett.51, 1127 (1983)Google Scholar
  4. 4.
    Rupeiner, G.: Phys. Rev. A20, 1608 (1979);24, 488 (1981);27, 1116 (1983); Phys. Rev. Lett.50, 287 (1983)Google Scholar
  5. 5.
    Salamon, P., Nulton, J., Ihrig, E.: J. Chem. Phys.80, 436 (1984)Google Scholar
  6. 6.
    Nulton, J., Salamon, P., Andresen, B., Qi Anmin: Quasistatic processes as step equilibrations. J. Chem. Phys. (submitted for publication)Google Scholar
  7. 7.
    Nulton, J., Salamon, P.: The geometry of the ideal gas. Phys. Rev. A (to appear)Google Scholar
  8. 8.
    Feldmann, T., Andresen, B., Anmin Qi, Salamon, P.: Thermodynamic lengths and intrinsic time scales in molecular relaxation. (draft) San Diego State University.Google Scholar
  9. 9.
    Salamon, P., Nulton, J.D., Berry, R.S.: Length in statistical thermodynamics. J. Chem. Phys. (to appear)Google Scholar
  10. 10.
    Flick, J.D., Salamon, P., Andresen, B.: Metric bounds on losses in adaptive coding. I.E.E.E. Transact. Inf. Theor. (submitted for publication)Google Scholar
  11. 11.
    Schlögl, F.: Z. Phys. B — Condensed Matter20, 177 (1975);22, 301 (1975);52, 51 (1983); Phys. Rep.62, 267 (1980)Google Scholar
  12. 12.
    Jaynes E.T.: Phys. Rev.106, 620 (1957)Google Scholar
  13. 13.
    Kullback, S.: Ann. Math. Stat.22, 79 (1951); Information theory and statistics. New York: Wiley 1951Google Scholar
  14. 14.
    Schlögl, F.: Z. Phys.191, 81 (1966);198, 560 (1967)Google Scholar
  15. 15.
    Salamon, P., Nulton, J., Feldmann, T., Andresen, B.: Relaxation times and metric bounds on dissipation (draft). San Diego State UniversityGoogle Scholar
  16. 16.
    Hatsopoulos, G.N., Keeman, J.H.: Principles of general thermodynamics. New York: J. Wiley 1965Google Scholar
  17. 17.
    Schlögl, F.: Z. Phys.191, 81 (1966);198, 559 (1967);249, 1 (1971)Google Scholar
  18. 18.
    Schlögl, F.: Z. Phys.244, 199 (1971);248, 446 (1971);249, 1 (1971); Phys. Lett.26A, 193 (1971); Progr. Theor. Phys. Suppl.64, 100 (1978); Z. Phys. B — Condensed Matter33, 199 (1979)Google Scholar
  19. 19.
    Ruppeiner, G.: Phys. Rev. A27, 1116 (1983)Google Scholar
  20. 20.
    Glansdorff, P., Prigogine, I.: Physica46, 344 (1970)Google Scholar
  21. 21.
    Schlögl, F.: Z. Phys.243, 303 (1971); Thermodynamics and regulation of biological processes. Lamprecht, L., Zotin, A.I., (eds.). Berlin, New York: de Gruyter, 1985Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • F. Schlögl
    • 1
  1. 1.Institut für Theoretische PhysikRheinisch-Westfälische Technische Hochschule AachenAachenGermany

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