Abstract
In the recent increasing interests in power-law behaviors beyond the usual exponential ones, there have been some concrete attempts in statistical physics to generalize the standard Boltzmann-Gibbs statistics. Among such generalizations, nonextensive statistical mechanics has been well studied for about the last two decades with many modifications and refinements. The generalization has provided not only a theoretical framework but also many applications such as chaos, multi-fractal, complex systems, nonequilibrium statistical mechanics, biophysics, econophysics, information theory and so on. At the same time as the developments in the generalization of statistical mechanics, the corresponding mathematical structures have also been required and uncovered. In particular, some deep connections to mathematical sciences such as q-analysis, information geometry, information theory and quantum probability theory have been revealed recently. These results obviously indicate an existence of the generalized mathematical structure including the mathematical framework for the exponential family as a special case, but the whole structure is still unclear.
In order to make an opportunity to discuss the mathematical structure induced from generalized entropies by scientists in many fields, the international workshop 'Mathematical Aspects of Generalized Entropies and their Applications' was held on 7–9 July 2009 at Kyoto TERRSA, Kyoto, Japan. This volume is the proceedings of the workshop which consisted of 6 invited speakers, 14 oral presenters, 7 poster presenters and 63 other participants. The topics of the workshop cover the nonextensive statistical mechanics, chaos, cosmology, information geometry, divergence theory, econophysics, materials engineering, molecular dynamics and entropy theory, information theory and so on. The workshop was organized as the first attempt to discuss these mathematical aspects with leading experts in each area.
We would like to express special thanks to all the invited speakers, the contributors and the participants at the workshop. We are also grateful to RIMS (Research Institute for Mathematical Science) in Kyoto University and the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (B), 18300003, 2009 for their support.
Organizing Committee
Editors of the Proceedings Hiroki Suyari (Chiba University, Japan) Atsumi Ohara (Osaka University, Japan) Tatsuaki Wada (Ibaraki University, Japan)
