Yugoslav Journal of Operations Research 2014 Volume 24, Issue 1, Pages: 145-155
https://doi.org/10.2298/YJOR120912031R
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Derivation of some new distributions in statistical mechanics using maximum entropy approach
Ray Amritansu (Department of Mathematics, Rajyadharpur Deshbandhu Vidyapith, Serampore, Hooghly, West Bengal, India)
Majumder S.K. (Department of Mathematics, Bengal Engineering and Science University (BESU), Shibpur, Howrah, West Bengal, India)
The maximum entropy principle has been earlier used to derive the Bose
Einstein(B.E.), Fermi Dirac(F.D.) & Intermediate Statistics(I.S.)
distribution of statistical mechanics. The central idea of these
distributions is to predict the distribution of the microstates, which are
the particle of the system, on the basis of the knowledge of some macroscopic
data. The latter information is specified in the form of some simple moment
constraints. One distribution differs from the other in the way in which the
constraints are specified. In the present paper, we have derived some new
distributions similar to B.E., F.D. distributions of statistical mechanics by
using maximum entropy principle. Some proofs of B.E. & F.D. distributions are
shown, and at the end some new results are discussed.
Keywords: Bose-Einstein (B.E.) distribution, Fermi-Dirac (F.D.) distribution, Lagrange’s multiplier, Shannons’ measure, Jaynes principle