0441885 20240103205825.320150319235959.9 11 s. P cav_un_epca*02930251212-074X2133 (2014)59-69 Tsallis entropy Gibbs random fields phase transitions Tsallis entropy rate cav_un_auth*0101114 Janžura Martin Stochastická informatika Department of Stochastic Informatics SI SI UTIA-B Department of Stochastic Informatics 100 Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2014/SI/janzura-0441885.pdf GBP402/12/G097 GA ČR CZ cav_un_auth*0281000 CEZ:AV0Z1075907 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. 2015 BB 1 http://hdl.handle.net/11104/0245437 S 2014 cav_un_epca*0293025 Bulletin of the Czech Econometric Society 1212-074X Roč. 21 č. 33 2014 59 69