, Volume 33, Issue 4, pp 455–465

Method of most probable distribution: New solutions and results

  • V J Menon
  • D C Agrawal
Statistical Mechanics

DOI: 10.1007/BF02846013

Cite this article as:
Menon, V.J. & Agrawal, D.C. Pramana - J Phys (1989) 32: 455. doi:10.1007/BF02846013


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 distributionvariational conditionsdigamma functionnon-Maxwellian tail



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