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Partition theory and thermodynamics of multi-dimensional oscillator assemblies

Published online by Cambridge University Press:  24 October 2008

V. S. Nanda
V. S. Nanda
Affiliation:
University of DelhiDelhiIndia
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Extract

The close similarity between the basic problems in statistical thermodynamics and the partition theory of numbers is now well recognized. In either case one is concerned with partitioning a large integer, under certain restrictions, which in effect means that the ‘Zustandsumme’ of a thermodynamic assembly is identical with the generating function of partitions appropriate to that assembly. The thermodynamic approach to the partition problem is of considerable interest as it has led to generalizations which so far have not yielded to the methods of the analytic theory of numbers. An interesting example is provided in a recent paper of Agarwala and Auluck (1) where the Hardy Ramanujan formula for partitions into integral powers of integers is shown to be valid for non-integral powers as well.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 47 , Issue 3 , July 1951 , pp. 591 - 601
Copyright
Copyright © Cambridge Philosophical Society 1951

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References

REFERENCES

(1)Agarwala, B. K. and Auluck, F. C. (In the Press.)Google Scholar
(2)Hardy, G. H. and Ramanujan, S.Proc. London Math. Soc. (2), 17 (1918), 75.CrossRefGoogle Scholar
(3)MacMahon, P. A.Combinatory analysis (Cambridge University Press, 1946), Sections ix, x and xi.Google Scholar
(4)Auluck, F. C. and Kothari, D. S.Proc. Cambridge Phil. Soc. 42 (1916), 272.CrossRefGoogle Scholar
(5)Hardy, G. H.Divergent series (Oxford University Press, 1949), p. 333.Google Scholar
(6)Dwight, H. B.Mathematical tables (McGraw Hill Book Co., 1941), p. 227.Google Scholar
(7)Chaundy, T. W.Quart. J. Math. 2 (1931), 234.CrossRefGoogle Scholar
(8)Wright, E. M.Quart. J. Math. 2 (1931), 177.CrossRefGoogle Scholar
(9)Brigham, N. A.Proc. Amer. Math. Soc. 1 (1950), 182.CrossRefGoogle Scholar