Complex Systems Seminar NONEXTENSIVE STATISTICAL MECHANICS AND CENTRAL LIMIT THEOREMS

Date
2006-11-20 15:00 - 2006-11-20 16:30
Place
auditorium,RIES,Hokkaido University
Speaker/Organizer
Constantino Tsallis(Centro Brasileiro de Pesquisas Fsicas,Brazil)
 
Boltzmann-Gibbs entropy and its associated statistical mechanicsaddress primarily thermal equilibrium, and, consistently, stronglychaotic nonlinear dynamical systems (positive maximal Lyapunovexponent, for classical systems). Its mathematical grounding isintimately related to the standard Central Limit Theorem. Nonextensivestatistical mechanics is a generalization of the Boltzmann-Gibbsconcepts which also focuses on various nonequlibrium states. Itsparadigmatic applicability emerges for weakly chaotic nonlinearsystems (vanishing maximal Lyapunov exponent, for classical systems).And it is related to generalized central limit theorems, whosecorresponding attractors are not necessarily Gaussians (or Levydistributions). A brief introduction to the whole subject will beprovided, as well as to some of its recent applications.Bibliography: (i) Europhysics News 36 (6) (Nov-Dec 2005 Special Issue,European Physical Society) http://www.europhysicsnews.com/ ; (ii)http://tsallis.cat.cbpf.br/biblio.htm ; (iii) C. Tsallis, M.Gell-Mann and Y. Sato, Proc. Natl. Acad. Sc. USA 102, 15377 (2005);(iv) L.G. Moyano, C. Tsallis and M. Gell-Mann, Europhys. Lett. 73, 813(2006); (v) S. Umarov, C. Tsallis and S. Steinberg, cond-mat/0603593;(vi) S. Umarov, C. Tsallis, M. Gell-Mann and S. Steinberg,cond-mat/0606038 and cond-mat/0606040.