, Volume 33, Issue 4, pp 455–465

Method of most probable distribution: New solutions and results

  • V J Menon
  • D C Agrawal
Statistical Mechanics


The variational conditions implied by the most probable equilibrium distribution for a dilute gas are set up exactly in terms of the digamma function without necessarily invoking a Stirling approximation. Through a sequence of lemmas it is proved that, at any given kinetic temperature, there are three classes of self-consistent solutions characterized by the parameterβ\( \beta \bar \gtrless 0 \) 0 and by non-Maxwellian tails. These ambiguities persist even for a free ideal gas.


Probable distribution variational conditions digamma function non-Maxwellian tail 




Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abramowitz M and Stegun I A (eds) 1972Handbook of mathematical functions (New York: Dover) p. 258, 259MATHGoogle Scholar
  2. Fleagle R J and Businger J A 1963An Introduction to atmospheric physics (New York: Academic) p. 28MATHGoogle Scholar
  3. Fonda L, Ghirardi G C and Rimini A 1978Rep. Prog. Phys. 41 587CrossRefADSGoogle Scholar
  4. Huang Kerson 1987Statistical mechanics (New York: Wiley) p. 79MATHGoogle Scholar
  5. Kennard E H 1938Kinetic theory of gases (New York: McGraw-Hill) p. 352Google Scholar
  6. Kittel C and Kroemer H 1980Thermal physics (San Francisco: Freeman) p. 460Google Scholar
  7. Zemansky M W and Dittman R H 1981Heat and thermodynamics (New York: McGraw-Hill) p. 278, 505Google Scholar

Copyright information

© Indian Academy of Sciences 1989

Authors and Affiliations

  • V J Menon
    • 1
  • D C Agrawal
    • 1
    • 2
  1. 1.Department of PhysicsBanaras Hindu UniversityVaranasiIndia
  2. 2.Department of Farm EngineeringBanaras Hindu UniversityVaranasiIndia

Personalised recommendations