Pesin-Type Identity for Weak Chaos

Physics – Condensed Matter – Statistical Mechanics

Scientific paper

Rate now

  [ 0.00 ] – not rated yet Voters 0   Comments 0

Details

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.

No associations

LandOfFree

Say what you really think

Search LandOfFree.com for scientists and scientific papers. Rate them and share your experience with other people.

Rating

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.

Rate now

     

Profile ID: LFWR-SCP-O-370564

  Search
All data on this website is collected from public sources. Our data reflects the most accurate information available at the time of publication.