Tsallis Entropy, Escort Probability and the Incomplete Information Theory

Non-extensive statistical mechanics appears as a powerful way to describe complex systems. Tsallis entropy, the main core of this theory has been remained as an unproven assumption. Many people have tried to derive the Tsallis entropy axiomatically. Here we follow the work of Wang (EPJB, 2002) and use the incomplete information theory to retrieve the Tsallis entropy. We change the incomplete information axioms to consider the escort probability and obtain a correct form of Tsallis entropy in comparison with Wang’s work.

[1]  Constantino Tsallis,et al.  Introduction to Nonextensive Statistical Mechanics and Thermodynamics , 2003 .

[2]  C. Tsallis,et al.  The role of constraints within generalized nonextensive statistics , 1998 .

[3]  Qiuping A. Wang.  Incomplete statistics: nonextensive generalizations of statistical mechanics , 2001 .

[4]  G. Mansoori,et al.  WHY NANOSYSTEMS AND MACROSCOPIC SYSTEMS BEHAVE DIFFERENTLY , 2018, 1804.09245.

[5]  A. Rényi.  On Measures of Entropy and Information , 1961 .

[6]  Amir H. Darooneh,et al.  Analysis of the spatial and temporal distributions between successive earthquakes: Nonextensive statistical mechanics viewpoint , 2008 .

[7]  Nonextensive scaling in a long-range Hamiltonian system , 2003, cond-mat/0311084.

[8]  D. Campos.  Rényi and Tsallis entropies for incomplete or overcomplete systems of events , 2010 .

[9]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[10]  Alfréd Rényi,et al.  Probability Theory , 1970 .

[11]  G. Ali Mansoori,et al.  Nonextensivity and Nonintensivity in Nanosystems: A Molecular Dynamics Simulation , 2005 .

[12]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[13]  Josiah Willard Gibbs.  Elementary Principles in Statistical Mechanics: ELEMENTARY PRINCIPLES IN STATISTICAL MECHANICS , 2010 .

[14]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[15]  Jan Naudts,et al.  Generalised Exponential Families and Associated Entropy Functions , 2008, Entropy.

[16]  A. Mehri,et al.  A nonextensive modification of the Gutenberg–Richter law: q-stretched exponential form , 2010 .

[17]  Jan Naudts,et al.  Parameter estimation in non-extensive thermostatistics , 2006 .

[18]  Remark on the escort distribution representation of nonextensive statistical mechanics , 2000, cond-mat/0006053.

[19]  Constantino Tsallis,et al.  Extensivity and entropy production , 2005 .

[20]  Amanda S. Barnard,et al.  Visualization of Hybridization in Nanocarbon Systems , 2005 .

[21]  J. R. Grigera,et al.  Extensive and non-extensive thermodynamics. A molecular dynamic test , 1996 .

[22]  Insurance pricing in small size markets , 2007 .

[23]  C. Tsallis,et al.  Escort mean values and the characterization of power-law-decaying probability densities , 2008, 0802.1698.

[24]  Qiuping A. Wang.  Nonextensive statistics and incomplete information , 2002 .

[25]  C. Tsallis.  Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World , 2009 .