2008/08/10 by Nickolay Korabel, Eli Barkai · 1 citation
Physics and Astronomy · #cond-mat.stat-mech #cond-mat.other #nlin.CD
paper · pdf · doi:10.1103/physrevlett.102.050601
published as Phys. Rev. Lett. 102, 050601 (2009) · 5 pages, 3 figures
arxiv created 2008/08/10 · arxiv updated 2009/12/01
Pesin's identity provides a profound connection between entropy hKS (statistical mechanics) and the Lyapunov exponent λ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby trajectories and then λ=0. In many cases such systems are non-ergodic and do not obey usual statistical mechanics. Here we investigate the non-ergodic phase of the Pomeau-Manneville map where separation of nearby trajectories follows δxt= δx0 eλα tα with 0<α<1. The limit distribution of λα is the inverse Lévy function. The average < λα > is related to the infinite invariant density, and most importantly to entropy. Our work gives a generalized Pesin's identity valid for systems with an infinite invariant density.