Nonextensive Statistical Mechanics

344 Bibliography20. A. Einstein, Theorie der Opaleszenz von homogenen Fl˙ussigkeiten undFl˙ussigkeitsgemischen in der Nȧhe des kritischen Zustandes, Annalen der Physik 33,1275 (1910). The translation is due to E.G.D. Cohen [21]. A slightly different translationalso is available: [“Usually W is put equal to the number of complexions... In orderto calculate W , one needs a complete (molecular-mechanical) theory of the systemunder consideration. Therefore it is dubious whether the Boltzmann principle has anymeaning without a complete molecular-mechanical theory or some other theory whichdescribes the elementary processes. S = R log W + const. seems without content, fromNa phenomenological point of view, without giving in addition such an Elementartheorie.”(Translation: Abraham Pais, Subtle is the Lord..., Oxford University Press, 1982)].21. E.G.D. Cohen, Boltzmann and Einstein: Statistics and Dynamics – An Unsolved Problem,Boltzmann Award Lecture at Statphys-Bangalore-2004, Pramana 64, 635 (2005).22. E.G.D. Cohen, Statistics and dynamics, Physica A 305, 19 (2002).23. E. Fermi, Thermodynamics (Dover, New York, 1936), page 53.24. E. Majorana, The value of statistical laws in physics and social sciences. The originalmanuscript in Italian was published by G. Gentile Jr. Scientia 36, 58 (1942), and was translatedinto English by R. Mantegna in 2005.25. C.E. Shannon, Bell System Tech. J. 27, 379 and 623 (1948); A Mathematical Theory ofCommunication, Bell Sys. Tech. J. 27, 379 and 623 (1948); and The Mathematical Theory ofCommunication (University of Illinois Press, Urbana, 1949).26. L. Tisza, Generalized Thermodynamics, (MIT Press, Cambridge, Massachusetts, 1961),page 123.27. P.T. Landsberg, Thermodynamics and Statistical Mechanics (Oxford University Press, NewYork, 1978; Dover, New York, 1990).28. P.T. Landsberg, Is equilibrium always an entropy maximum?, J. Stat. Phys. 35, 159 (1984).29. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam,1981).30. L.G. Taff, Celestial Mechanics (Wiley, New York, 1985).31. W.C. Saslaw, Gravitation Physics of Stellar and Galactic Systems (Cambridge UniversityPress, Cambridge, 1985).32. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanics, (John Wiley and Sons,New York, 1975).33. D. Ruelle, Thermodynamic Formalism – The Mathematical Structures of Classical EquilibriumStatistical Mechanics, Vol. 5 of Encyclopedia of Mathematics and its Applications(Addison-Wesley Publishing Company, Reading, Massachusetts, 1978); 2nd edition, ThermodynamicFormalism – The Mathematical Structures of Equilibrium Statistical Mechanics,(Cambridge University Press, Cambridge, 2004).34. F. Takens, in Structures in Dynamics – Finite Dimensional Deterministic Studies, eds.H.W. Broer, F. Dumortier, S.J. van Strien and F. Takens, p. 253 (North-Holland, Amsterdam,1991).35. R. Balian, From Microphysics to Macrophysics (Springer-Verlag, Berlin, 1991), pages 205and 206. The original French edition: Du microscopique au macroscopique, Cours de l’ EcolePolytechnique (Ellipses, Paris, 1982).36. J. Maddox, When entropy does not seem extensive,Nature365, 103 (1993).37. M. Srednicki, Entropy and area, Phys. Lett. 71, 666 (1993).38. A.C.D. van Enter, R. Fernandez and A.D. Sokal, Regularity properties and pathologies ofposition-space renormalization-group transformations: Scope and limitations of gibbsiantheory, J. Stat. Phys. 72, 879 (1993).39. C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J.Stat.Phys.52, 479(1988).40. C. Tsallis, Nonextensive statistical mechanics and nonlinear dynamics, inInterdisciplinaryAspects of Turbulence, eds. W. Hillebrandt and F. Kupka, Lecture Notes in Physics 756, 21(Springer, Berlin, 2008).