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## Discussiones Mathematicae Probability and Statistics

2000 | 20 | 2 | 167-176
Tytuł artykułu

### Canonical distributions and phase transitions

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Entropy maximization subject to known expected values is extended to the case where the random variables involved may take on positive infinite values. As a result, an arbitrary probability distribution on a finite set may be realized as a canonical distribution. The Rényi entropy of the distribution arises as a natural by-product of this realization. Starting with the uniform distributionon a proper subset of a set, the canonical distribution of equilibriumstatistical mechanics may be used to exhibit an elementary phase transition, characterized by discontinuity of the partition function.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
167-176
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-02-03
poprawiono
2000-03-15
Twórcy
autor
• School of Operations Research and Industrial Engineering Cornell University, Ithaca, NY 14853, USA
autor
• Department of Mathematics, Iowa State University, Ames, IA 50011, USA
Bibliografia
• [1] J.W. Gibbs, Elementary Principles in Statistical Mechanics Developed with Especial Reference to the Rational Foundation of Thermodynamics, Yale University Press New Haven, CT 1902.
• [2] E.T. Jaynes, Information theory and statistical mechanics, Phys. Rev. 106 (1957), 620.
• [3] M. Tribus, Rational Descriptions, Decisions and Designs Pergamon, Elmsford, NY 1969.
• [4] R.D. Levine and M. Tribus (eds.), The Maximum Entropy Formalism, MIT Press, Cambridge, MA 1979.
• [5] J.H. Justice (ed.), Maximum Entropy and Bayesian Methods in Applied Statistics, Cambridge University Press, Cambridge 1986.
• [6] W.T. Grandy, Jr, Foundations of Statistical Mechanics, Volume I, Reidel, Dordrecht 1987.
• [7] A. Rényi, On measures of entropy and information, Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability 1960, Volume 1, University of California Press, Berkeley, CA 1961.
• [8] J. Aczél, Measuring information beyond information theory - why some generalized information measures may be useful, others not, Aequationes Math. 27 (1984), 1.
• [9] W. Pauli, Die allgemeinen Prinzipien der Wellenmechanik, Handbuch der Physik, Bd. 24/1 Quantentheorie'', Springer, Berlin 1933.
• [10] C. Shannon, A mathematical theory of communication, Bell Systems Technical Journal 23 (1948), 349.
• [11] K.B. Athreya, Entropy maximization, IMA Preprint Series # 1231, Institute for Mathematics and its Applications, University of Minnesota, Minneapolis, MN 1994.
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Bibliografia
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