Nonextensive Statistical Mechanics

5.2 Low-Dimensional Conservative Maps 171Fig. 5.20 Numerical study of the baker map, with controlled fixed precision. The sequences of thetop figure exhibit the evolution in phase-space with a fixed precision. The corresponding curvesfor S 1 (t) areshowninthebottom figure. The evolution of S 1 (t) corresponding to a higher fixedprecision experiment (40 digits) is shown as well; the time reversal of the entropy is not observedbefore t = 100 (from [138]).average. The temperature associated with the uniform ensemble (that we will callBG temperature T BG because of its similarity with the equal-a-priori-probabilitypostulate) is given by T BG = ∫ 10 dp p2 − ( ∫ 10 dp p2 ) = 1/12. Notice that, in thepresent conservative model, the “temperature” T is necessarily bounded since pitself is bounded, in contrast with a true thermodynamical temperature, which is ofcourse unbounded. The time evolution of the system and of T , for typical values ofa are depicted in Fig. 5.21.