Nonextensive Statistical Mechanics

Bibliography 34784. A.N. Kolmogorov, Dok. Acad. Nauk SSSR 119, 861 (1958); Ya. G. Sinai, Dok. Acad. NaukSSSR 124, 768 (1959).85. V. Latora and M. Baranger, Phys. Rev. Lett. 82, 520 (1999).86. Ya. Pesin, Russ. Math. Surveys 32, 55 (1977); Ya. Pesin in Hamiltonian Dynamical Systems:A Reprint Selection, eds. R.S. MacKay and J.D. Meiss (Adam Hilger, Bristol, 1987).87. S. Kullback and R.A. Leibler, Ann. Math. Stat. 22, 79 (1961); S.L. Braunstein, Phys. Lett. A219, 169 (1996).88. C. Tsallis, Generalized entropy-based criterion for consistent testing, Phys. Rev. E 58, 1442(1998).89. W.K. Wootters, Phys. Rev. D 23, 357 (1981).90. Robinson, Rev. Econ. Studies 58, 437 (1991).91. W. Brock, D. Dechert and J. Scheinkman (unpublished).92. L. Borland, A.R. Plastino and C. Tsallis, Information gain within nonextensive thermostatistics,J. Math. Phys. 39, 6490 (1998); [Errata: J. Math. Phys. 40, 2196 (1999)].93. P.W. Lamberti and A.P. Majtey, Non-logarithmic Jensen-Shannon divergence, Physica A 329,81 (2003).94. A.P. Majtey, P.W. Lamberti and A. Plastino, A monoparametric family of metrics for statisticalmechanics, Physica A 344, 547 (2004).95. S. Amari and H. Nagaoka, Methods of Information Geometry, SeriesTranslations of MathematicalMonographs 191 (Oxford University Press, Oxford, 2000), [Eq. (3.80) in page 72for the triangle equality].96. A. Dukkipati, M.N. Murty and S. Bhatnagar, Nonextensive triangle equality and other propertiesof Tsallis relative-entropy minimization, Physica A 361, 124-138 (2005).97. M.E. Fisher, Arch. Rat. Mech. Anal. 17, 377 (1964), J. Chem. Phys. 42, 3852 (1965) andJ. Math. Phys. 6, 1643 (1965).98. M.E. Fisher and D. Ruelle, J. Math. Phys. 7, 260 (1966).99. M.E. Fisher and J.L. Lebowitz, Commun. Math. Phys. 19, 251 (1970).100. F. Baldovin, L.G. Moyano and C. Tsallis, Boltzmann-Gibbs thermal equilibrium distributionfor classical systems and Newton law: A computational discussion, Europhys. J. B 52,113 (2006).101. G. Gentile, Nuovo Cimento 17, 493 (1940); Nuovo Cimento 19, 109 (1942).102. M.C.S. Vieira and C. Tsallis, D-dimensional ideal gas in parastatistics: Thermodynamicproperties,J.Stat.Phys.48, 97 (1987).103. H.S. Robertson, Statistical Thermophysics (Prentice-Hall, Englewood Cliffs, New Jersey,1993).104. C. Tsallis, What are the numbers that experiments provide?, QuimicaNova17, 468 (1994).105. S. Watanabe, Knowing and Guessing (Wiley, New York, 1969).106. H. Barlow, Conditions for versatile learning, Helmholtz’s unconscious inference, and thetask of perception, Vision. Res. 30, 1561 (1990).107. J. Havrda and F. Charvat, Kybernetika 3, 30 (1967) were apparently the first to ever introducethe entropic form of Eq. (3.18), though with a different prefactor, adapted to binary variables.I. Vajda, Kybernetika 4, 105 (1968) [in Czeck] further studied this form, quoting Havrda andCharvat. Z. Daroczy, Inf. Control 16, 36 (1970) rediscovered this form (he quotes neitherHavrda-Charvat nor Vajda). J. Lindhard and V. Nielsen, Studies in statistical mechanics,DetKongelige Danske Videnskabernes Selskab Matematisk-fysiske Meddelelser (Denmark) 38(9), 1 (1971) rediscovered this form (they quote none of the predecessors) through the propertyof entropic composability. B.D. Sharma and D.P. Mittal, J. Math. Sci. 10, 28 (1975) introduceda two-parameter form which reproduces both S q and Renyi entropy [108] as particularcases. J. Aczel and Z. Daroczy [On Measures of Information and Their Characterization, inMathematics in Science and Engineering, ed. R. Bellman (Academic Press, New York, 1975)]quote Havrda-Charvat and Vajda, but not Lindhard-Nielsen. A. Wehrl, Rev. Mod. Phys. 50,221 (1978) mentions the form of S q in page 247, quotes Daroczy, but ignores Havrda-Charvat,Vajda, Lindhard-Nielsen, and Sharma-Mittal. In 1979, the entropic form S q was proposedfor ecological purposes by G.P. Patil and C. Taillie, An overview of diversity, in Ecological