On the Tsallis Entropy for Gibbs Random Fields

0441885 - ÚTIA 2015 RIV CZ eng J - Journal Article
Janžura, Martin
On the Tsallis Entropy for Gibbs Random Fields.
Bulletin of the Czech Econometric Society. Roč. 21, č. 33 (2014), s. 59-69. ISSN 1212-074X
R&D Projects: GA ČR(CZ) GBP402/12/G097
Institutional research plan: CEZ:AV0Z1075907
Keywords : Tsallis entropy * Gibbs random fields * phase transitions * Tsallis entropy rate
Subject RIV: BB - Applied Statistics, Operational Research
http://library.utia.cas.cz/separaty/2014/SI/janzura-0441885.pdf

The Tsallis entropy, as a generalization of the standard Shannon-type entropy, was introduced by Constantino Tsallis (1988). Since that the concept has been extensively studied (see, e.g., Tsallis (2009)). In the present paper we address the problem of generalizing the concept for innite- dimensional systems, i.e., the random processes and elds. Apparently, rather well suited models are the Gibbs distributions (cf. e.g., Georgii (1988)). We construct the appropriate Tsallis entropy rate either asymptotically by limit over a sequence of expanding volumes or by analogy with the exponential nite-dimensional distributions. Basic properties, taking into account the possible phase transitions, are also introduced.
Permanent Link: http://hdl.handle.net/11104/0245437