Dukkipati, Ambedkar and Bhatnagar, Shalabh and Murty, Narasimha M
(2007)
*On measure-theoretic aspects of nonextensive entropy functionals and corresponding maximum entropy prescriptions.*
In: Physica A: Statistical Mechanics and its Applications, 384
(2).
pp. 758-774.

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## Abstract

Shannon entropy of a probability measure P, defined as $- \int_X(dp/d \mu) \hspace{2} ln (dp/d \mu)d \mu $ on a measure space $ (X, m,\mu )$ source, is not a natural extension from the discrete case. However, maximum entropy (ME) prescriptions of Shannon entropy functional in the measure-theoretic case are consistent with those for the discrete case. Also it is well known that Kullback–Leibler relative entropy can be extended naturally to measure-theoretic case. In this paper, we study the measure-theoretic aspects of nonextensive (Tsallis) entropy functionals and discuss the ME prescriptions. We present two results in this regard: (i) we prove that, as in the case of classical relative-entropy, the measure-theoretic definition of Tsallis relative-entropy is a natural extension of its discrete case, and (ii) we show that ME-prescriptions of measure-theoretic Tsallis entropy are consistent with the discrete case with respect to a particular instance of ME.

Item Type: | Journal Article |
---|---|

Publication: | Physica A: Statistical Mechanics and its Applications |

Publisher: | Elsevier |

Additional Information: | Copyright of this article belongs to Elsevier. |

Keywords: | Measure space;Tsallis entropy;Maximum entropy distribution; |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 19 Nov 2007 |

Last Modified: | 19 Sep 2010 04:41 |

URI: | http://eprints.iisc.ac.in/id/eprint/12530 |

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