Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2008-08-10
Phys. Rev. Lett. 102, 050601 (2009)
Physics
Condensed Matter
Statistical Mechanics
5 pages, 3 figures
Scientific paper
10.1103/PhysRevLett.102.050601
Pesin's identity provides a profound connection between entropy $h_{KS}$ (statistical mechanics) and the Lyapunov exponent $\lambda$ (chaos theory). It is well known that many systems exhibit sub-exponential separation of nearby trajectories and then $\lambda=0$. 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 $\delta x_t= \delta x_0 e^{\lambda_{\alpha} t^{\alpha}}$ with $0<\alpha<1$. The limit distribution of $\lambda_{\alpha}$ is the inverse L{\'e}vy function. The average $< \lambda_{\alpha} >$ 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.
Barkai Eli
Korabel Nickolay
No associations
LandOfFree
Pesin-Type Identity for Weak Chaos does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Pesin-Type Identity for Weak Chaos, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pesin-Type Identity for Weak Chaos will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-370564