A Generalized Form of the New Statistics

S. Chandrasekhar
Phys. Rev. 34, 1204 – Published 15 October 1929
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Abstract

Instead of assuming the probabilities of absorption and emission of atoms in a radiation field as equal to Baρ and A+Beρ (the well-known Einstein equations) Strum has in a recent paper assumed them to be respectively equal to Baρ+Caρ2+ and A+Beρ+Ceρ2+. This leads to a modification of Planck's law. It is shown in this paper that this assumption effectively amounts to replacing the new statistical law of interaction of Nordheim e.g. f1±f*Af1*1±f1*A1 by the more general (f+af2+)1±f*A±af*2A±(f1+af12+)1±f1*A1±af1*2A1± where f, f1, f*, f1* are the distribution functions for the projectiles corresponding to the numbers of each before and after collision; A, A1 the number of cells respectively associated with them. On this basis a general H function defined by H=(f+af2+) log(f+af2+)(A±f±af2±)log(A±f±af2±) is considered. As a consequence of this we get a generalized distribution function given by the relation f+af2+bf3+=ACexp[c|v|2]1 If we take only two terms we get approximately J=ACec|v|21A2a(Cec|v|21)2=ACexp[c|v|2]1A2a(Cexp[c|v|2]1)2. By substituting the appropriate values for A in the cases corresponding to the photons and the atoms, we get Strum's modified radiation formula, and a new distribution function for a gas. Thus as a result of a generalized analysis of the H-theorem we get a new statistics the successive approximations of which are a more accurate statistics which includes Strum's formula, the statistics of Bose-Einstein, Fermi-Dirac, the classical statistics of Maxwell-Boltzmann. It is suggested that this new statistics may be of importance in the study of dense matter at high temperature.

  • Received 1 July 1929

DOI:https://doi.org/10.1103/PhysRev.34.1204

©1929 American Physical Society

Authors & Affiliations

S. Chandrasekhar

  • Presidency College, Madras, India

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Issue

Vol. 34, Iss. 8 — October 1929

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