Nonextensive Statistical Mechanics

Chapter 3Generalizing What We Learnt: NonextensiveStatistical MechanicsDon Quijote me ha revelado íntimos secretos suyos que noreveló a CervantesVíctor Goti(Prólogo de Niebla de Miguel de Unamuno, 1935)3.1 Playing with Differential Equations – A MetaphorAs we already emphasized, there is no logical-deductive procedure for generalizingany physical theory. This occurs through all types of paths that, in one way or another,are ultimately but metaphors. Let us present here a possible metaphor forgeneralizing the BG entropy.The simplest ordinary differential equation can be considered to beIts solution isdydxwhose symmetric curve with regard to the bissector axis is= 0 (y(0) = 1) . (3.1)y = 1 , (3.2)x = 1 . (3.3)As the second simplest differential equation we might considerIts solution isdydx= 1 (y(0) = 1) . (3.4)y = 1 + x , (3.5)C. Tsallis, Introduction to Nonextensive Statistical Mechanics,DOI 10.1007/978-0-387-85359-8 3, C○ Springer Science+Business Media, LLC 200937