On Conditional Tsallis Entropy

Andreia Teixeira; André Souto; Luís Antunes

doi:10.3390/e23111427

On Conditional Tsallis Entropy

Entropy (Basel). 2021 Oct 29;23(11):1427. doi: 10.3390/e23111427.

Authors

Andreia Teixeira^{1

2

3}, André Souto^{4

5

6}, Luís Antunes⁷

Affiliations

¹ CINTESIS-Centre for Health Technology and Services Research, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal.
² MEDCIDS-Department of Community Medicine, Information and Decision in Health, Faculty of Medicine, University of Porto, 4200-450 Porto, Portugal.
³ ADiT-LAB, Instituto Politécnico de Viana do Castelo, Rua Escola Industrial e Comercial Nun'Álvares, 4900-347 Viana do Castelo, Portugal.
⁴ LASIGE, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal.
⁵ Departamento de Informática, Faculdade de Ciências da Universidade de Lisboa, Campo Grande, 1749-016 Lisboa, Portugal.
⁶ Instituto de Telecomunicações, Av. Rovisco Pais, n 1, 1049-001 Lisboa, Portugal.
⁷ Computer Science Department, Faculty of Sciences, University of Porto, Rua do Campo Alegre, 4169-007 Porto, Portugal.

Abstract

There is no generally accepted definition for conditional Tsallis entropy. The standard definition of (unconditional) Tsallis entropy depends on a parameter α that converges to the Shannon entropy as α approaches 1. In this paper, we describe three proposed definitions of conditional Tsallis entropy suggested in the literature-their properties are studied and their values, as a function of α, are compared. We also consider another natural proposal for conditional Tsallis entropy and compare it with the existing ones. Lastly, we present an online tool to compute the four conditional Tsallis entropies, given the probability distributions and the value of the parameter α.

Keywords: Generalizations of Shannon entropy; Tsallis entropy; conditional Tsallis entropies.