%0 Book Section %1 statphys23_0479 %A Lopez, G. Ruiz %A Tsallis, C. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K attractors chaos dynamics effects mechanics nonextensive nonlinear precision statistical statphys23 topic-5 weak %T Entropy production and roundoff-induced attractors in conservative maps %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=479 %X We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore Phys Rev Lett 64, 2354 (1990). The time evolution of the entropy $S_q 1-\sum_i=1^Wp_i^qq-1$ ($S_1=S_BG-\sum_i=1^Wp_i p_i$) is studied and we exhibit the dramatic effect introduced by numerical precision. In spite of being area-preserving maps, both maps present unexpected pseudo-attractors related to zero Lebesgue-measure effects associated with the frontiers existing in the definition of the map, which gradually disappear for increasingly large precision. We also observe that, consistently with the results by V. Latora and M. Baranger Phys. Rev. Lett. 82, 520 (1999), the rate of the far-from-equilibrium entropy production of the baker map, numerically coincides with the standard Kolmogorov-Sinai entropy of this strongly chaotic system.

@incollection{statphys23_0479, abstract = {We numerically study two conservative two-dimensional maps, namely the baker map (whose Lyapunov exponent is known to be positive), and a typical one (exhibiting a vanishing Lyapunov exponent) chosen from the generalized shift family of maps introduced by C. Moore [Phys Rev Lett {\bf 64}, 2354 (1990)]. The time evolution of the entropy $S_q \equiv \frac{1-\sum_{i=1}^Wp_i^q}{q-1}$ ($S_1=S_{BG}\equiv -\sum_{i=1}^Wp_i \ln p_i$) is studied and we exhibit the dramatic effect introduced by numerical precision. In spite of being area-preserving maps, both maps present unexpected {\it pseudo-attractors} related to zero Lebesgue-measure effects associated with the frontiers existing in the definition of the map, which gradually disappear for increasingly large precision. We also observe that, consistently with the results by V. Latora and M. Baranger [Phys. Rev. Lett. {\bf 82}, 520 (1999)], the rate of the far-from-equilibrium entropy production of the baker map, numerically coincides with the standard Kolmogorov-Sinai entropy of this strongly chaotic system.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lopez, G. Ruiz and Tsallis, C.}, biburl = {https://www.bibsonomy.org/bibtex/2739d98b02bfeaf5f6b4fa60bf96703b5/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {306a05bcab36967594689e8440dc1e97}, intrahash = {739d98b02bfeaf5f6b4fa60bf96703b5}, keywords = {attractors chaos dynamics effects mechanics nonextensive nonlinear precision statistical statphys23 topic-5 weak}, month = {9-13 July}, timestamp = {2007-06-20T10:16:21.000+0200}, title = {Entropy production and roundoff-induced attractors in conservative maps}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=479}, year = 2007 }