Statistical mechanical characterization of billiard systems

Reminiscences of Half a Century of Life in the World of Theoretical Physics

“…An important one is indicated in Figure 10, which illustrates the Enciso-Tempesta theorem [61], proving that the only entropic functional which simultaneously is traceform and composable, and contains the BG entropy as a particular case is S q as given in Equation ( 6). In the realm of nonlinear dynamical systems, we may think of the three classical roads to chaos (period doubling, quasi-periodicity and intermittency) as one more triplet deeply related to q-statistics, as profusely shown by Robledo, Tirnakli, Beck, Jensen and their collaborators (see [62][63][64][65][66][67] and references therein), among others. Another interesting triangle emerged in [68] in connection with molecular kinetics as shown in Figure 11.…”