Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

For a probability distribution $P$, Renyi fractal dimension is defined as

$$D_q = \lim_{\epsilon\rightarrow 0} \frac{R_q(P_\epsilon)}{\log(1/\epsilon)},$$ where $R_q$ is Renyi entropy of order $q$ and $P_\epsilon$ is the coarse-grained probability distribution (i.e. put in boxes of linear size $\epsilon$).

The question is if there are any phenomena, for which using non-trivial $q$ (i.e. $q\neq0,1,2,\infty$) is beneficial or naturally preferred?

share|cite|improve this question

The Rényi entropy of order $q = \frac{1}{2}$ apperas in several measures of pure states entanglement, please see for example: Karol Zyczkowski, Ingemar Bengtsson: Relatively Pure states entanglement. This entropy has the property that for three state systems, the equientropy trajectories form circles with respect to the the Bhattacharyya distance, please see for example: Bengtsson Zyczkowski: Geometry of quantum states, page 57.

share|cite|improve this answer
Thank you for a nice example. However, $q=1/2$ is semi-trivial (as it is conjugated to $q=\infty$). – Piotr Migdal Dec 16 '11 at 10:21

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.