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GENERALIZED MEASURE OF UNCERTAINTY AND THE MAXIMIZABLE ENTROPY

CONGJIE OU

College of Information Science and Engineering, Huaqiao University, Quanzhou 362021, China

Institut Suprieur des Matériaux et Mécaniques Avancés du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France

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AZIZ EL KAABOUCHI

Institut Suprieur des Matériaux et Mécaniques Avancés du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France

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JINCAN CHEN

Institut Suprieur des Matériaux et Mécaniques Avancés du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France

Department of Physics and Institute of Theoretical Physics and Astrophysics, Xiamen University, Xiamen 361005, China

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ALAIN LE MÉHAUTÉ

Institut Suprieur des Matériaux et Mécaniques Avancés du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France

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, and

ALEXANDRE QIUPING WANG

Institut Suprieur des Matériaux et Mécaniques Avancés du Mans, 44, Avenue F.A. Bartholdi, 72000 Le Mans, France

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https://doi.org/10.1142/S0217984910022883Cited by:4 (Source: Crossref)

Abstract

For a random variable x we can define a variational relationship with practical physical meaning as , where I is the uncertainty measure. With the help of a generalized definition of expectation, , we can find the concrete forms of the maximizable entropies for any given probability distribution function, where g({p_i}) may have different forms for different statistical methods which include the extensive and non-extensive statistics. Moreover, it is pointed out that this generalized uncertainty measure is valid not only for thermodynamic systems but also for non-thermodynamic systems.

Keywords:

PACS: 02.50.-r, 65.40.gd, 05.90.+m

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