Nonextensive Statistical Mechanics

346 Bibliography64. S. Abe and Y. Okamoto, eds., Nonextensive Statistical Mechanics and Its Applications,SeriesLecture Notes in Physics (Springer, Berlin, 2001).65. P. Grigolini, C. Tsallis and B.J. West, eds., Classical and Quantum Complexity and NonextensiveThermodynamics, Chaos, Solitons and Fractals 13, Issue 3 (2002).66. G. Kaniadakis, M. Lissia and A. Rapisarda, eds., Non Extensive Thermodynamics and PhysicalApplications, Physica A 305, 1/2 (2002).67. M. Sugiyama, ed., Nonadditive Entropy and Nonextensive Statistical Mechanics, ContinuumMechanics and Thermodynamics 16 (Springer-Verlag, Heidelberg, 2004).68. H.L. Swinney and C. Tsallis, eds., Anomalous Distributions, Nonlinear Dynamics andNonextensivity, Physica D 193, Issue 1 (2004).69. M. Gell-Mann and C. Tsallis, eds., Nonextensive Entropy – Interdisciplinary Applications(Oxford University Press, New York, 2004).70. G. Kaniadakis and M. Lissia, eds., News and Expectations in Thermostatistics, Physica A340, Issue 1 (2004).71. H.J. Herrmann, M. Barbosa and E.M.F. Curado, eds., Trends and perspectives in extensiveand non-extensive statistical mechanics, Physica A 344, Issue 3/4 (2004).72. C. Beck, G. Benedek, A. Rapisarda and C. Tsallis, eds., Complexity, Metastability andNonextensivity (World Scientific, Singapore, 2005).73. J.P. Boon and C. Tsallis, eds., Nonextensive Statistical Mechanics: New Trends, New Perspectives,Europhys. News 36, Issue 6, 183 (EDP Sciences, Paris, 2005).74. G. Kaniadakis, A. Carbone and M. Lissia, eds., News, expectations and trends in statisticalphysics, Physica A 365, Issue 1 (2006).75. S. Abe, M. Sakagami and N. Suzuki, eds., Complexity and Nonextensivity - New Trends inStatistical Mechanics, Prog. Theor. Phys. Suppl. 162 (Physical Society of Japan, 2006).76. S. Abe, H. Herrmann, P. Quarati, A. Rapisarda and C. Tsallis, eds., Complexity, Metastabilityand Nonextensivity, American Institute of Physics Conference Proceedings 965 (New York,2007).77. S. Martinez, F. Nicolas, F. Pennini and A. Plastino, Tsallis’ entropy maximization procedurerevisited, Physica A 286, 489 (2000).78. Ancient and popular Greek expression. A possible translation into English is “All things intheir proper measure are excellent”. The expression is currently attributed to Kleoboulos ofLindos (one of the seven philosophers of Greek antiquity), although in a more laconic – andlogically equivalent – version, namelyIndeed, it is this abridged form that Clement of Alexandria (Stromata, 1.14.61) and DiogenesLaertius (Lives of Philosophers, Book 1.93, Loeb Series) attribute to Kleoboulos. To me, thisexpression addresses what I consider the basis of all variational principles, in my opinionthe most elegant form in which physical laws can be expressed. The Principle of least actionin mechanics, and the Optimization of the entropy in statistical mechanics, are but suchrealizations.79. B. Lesche, Instabilities of Renyi entropies, J.Stat.Phys.27, 419 (1982). Lesche himselfcalled stability this property. Two decades later, in personal conversation, I argued with himthat that name could be misleading in the sense that it seems to suggest some relation withthermodynamical stability, with which it has no mathematical connection (thermodynamicalstability has, in fact, connection with concavity). I suggested the use of experimental robustnessinstead. Lesche fully agreed that it is a better name. Consistently, I use it preferentlysince then.80. S. Abe, B. Lesche and J. Mund, How should the distance of probability assignments bejudged?, J.Stat.Phys.128, 1189 (2007).81. A.I. Khinchin, Uspekhi matem. Nauk8, 3 (1953) (R.A. Silverman, M.D. Friedman, trans.,Mathematical Foundations of Information Theory, Dover, New York, 1957).82. S.H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistryand Engineering (Perseus Books Publishing, Cambridge, MA, 1994).83. E. Ott, Chaos in Dynamical Systems, Second Edition (Cambridge University Press,Cambridge, 2002).