A Note on Burg’s Modified Entropy in Statistical Mechanics

Amritansu Ray and S. K. Majumder
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Amritansu Ray: Department of Mathematics, Rajyadharpur Deshbandhu Vidyapith, Serampore, Hooghly 712203, West Bengal, India
S. K. Majumder: Department of Mathematics, Indian Institute of Engineering Science and Technology (IIEST), Shibpur, Howrah 711103, West Bengal, India

Mathematics, 2016, vol. 4, issue 1, 1-17

Abstract: Burg’s entropy plays an important role in this age of information euphoria, particularly in understanding the emergent behavior of a complex system such as statistical mechanics. For discrete or continuous variable, maximization of Burg’s Entropy subject to its only natural and mean constraint always provide us a positive density function though the Entropy is always negative. On the other hand, Burg’s modified entropy is a better measure than the standard Burg’s entropy measure since this is always positive and there is no computational problem for small probabilistic values. Moreover, the maximum value of Burg’s modified entropy increases with the number of possible outcomes. In this paper, a premium has been put on the fact that if Burg’s modified entropy is used instead of conventional Burg’s entropy in a maximum entropy probability density (MEPD) function, the result yields a better approximation of the probability distribution. An important lemma in basic algebra and a suitable example with tables and graphs in statistical mechanics have been given to illustrate the whole idea appropriately.

Keywords: entropy optimization; probability distribution; Shannon’s Entropy; Burg’s Entropy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2016
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