Advertisement

Pramana

, Volume 17, Issue 6, pp 509–514 | Cite as

Extensivity of entropy and modern form of Gibbs paradox

  • D Home
  • S Sengupta
Statistical Physics

Abstract

The extensivity property of entropy is clarified in the light of a critical examination of the entropy formula based on quantum statistics and the relevant thermodynamic requirement. The modern form of the Gibbs paradox, related to the discontinuous jump in entropy due to identity or non-identity of particles, is critically investigated. Qualitative framework of a new resolution of this paradox, which analyses the general effect of distinction mark on the Hamiltonian of a system of identical particles, is outlined.

Keywords

Extensivity of entropy Gibbs paradox distinguishability identical particles Hamiltonian 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bridgman P W 1961 The Nature of thermodynamics (University Press: Cambridge, Mass p. 169Google Scholar
  2. Casper B M and Freier S 1973 Am. J. Phys. 41 509CrossRefADSGoogle Scholar
  3. Ehrenfest O P and Trkal V 1921 Ann. Physik 65 609CrossRefADSGoogle Scholar
  4. Fong P 1963 Foundations of thermodynamics (New York: Oxford University Press)zbMATHGoogle Scholar
  5. Fowler R H 1966 Statistical mechanics (London: Cambridge University Press) pp. 205–206Google Scholar
  6. Gibbs J W 1931 The collected works (London: Longman, Green) Part I, pp. 187–207Google Scholar
  7. Huang K 1963 Statistical mechanics (New York: John Wiley) pp. 153–154Google Scholar
  8. Jackson E A 1968 Equilibrium statistical mechanics (Englewood Cliffs, N J: Prentice Hall, pp. 229–231zbMATHGoogle Scholar
  9. Klein M J 1958 Am. J. Phys. 26 80zbMATHCrossRefADSGoogle Scholar
  10. Lande A 1960 From dualism to unity in quantum physics (London: Cambridge University Press)zbMATHGoogle Scholar
  11. Landsberg P T 1961 Thermodynamics with quantum statistical illustrations (New York: Interscience Publishers) pp. 128–142zbMATHGoogle Scholar
  12. Landsberg P T and Tranah D 1978 Am. J. Phys. 46 228CrossRefADSGoogle Scholar
  13. Landsberg P T and Tranah D 1980 Collect. phenom. 3 73MathSciNetGoogle Scholar
  14. Münster A 1969 Statistical thermodynamics (Berlin-Springer-Verlag) Vol. 1, pp. 212–256Google Scholar
  15. Penrose O 1970 Foundations of statistical mechanics (New York: Pergamon Press) pp. 171–172zbMATHGoogle Scholar
  16. Reif F 1965 Fundamentals of statistical and thermal physics (New York: McGraw-Hill), pp. 243–244Google Scholar
  17. Schrödinger E 1967 Statistical thermodynamics (London: Cambridge University Press)Google Scholar
  18. Sommerfeld A 1965 Thermodynamics and statistical mechanics (New York: Academic Press)Google Scholar
  19. Sudarshan E C G and Mehra J 1970 Int. J. Theor. Phys. 3 245CrossRefGoogle Scholar
  20. Von Neumann J 1955 Mathematical foundations of quantum mechanics (Princeton, N.J: Princeton University Press), pp. 370–379zbMATHGoogle Scholar
  21. Wright P G 1970 Proc. R. Soc. London A317 487ADSGoogle Scholar
  22. Yourgrau W, Merwe A and Raw G 1966 A treatise on irreversible and statistical thermophysics (New York: Macmillan), pp. 235–241Google Scholar

Copyright information

© Indian Academy of Sciences 1981

Authors and Affiliations

  • D Home
    • 1
  • S Sengupta
    • 1
  1. 1.Solid State Physics Research Centre, Physics DepartmentPresidency CollegeCalcuttaIndia

Personalised recommendations