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4
votes
1answer
414 views

Infinitely Divisible Distributions and Maximal Entropy

The normal distribution on $\mathbb{R}$, the exponential distribution on $\mathbb{R}_{\geq 0}$, and the geometric distribution on $\mathbb{N}$ are examples of distributions that are both infinitely ...
8
votes
1answer
1k views

Entropy of first return map and suspension flows

There are some well know formulas of Abramov about derived systems. Firstly let $(X,\mu,f)$ be a probability preserving system and $A\subset X$ is measurable such that $\bigcup_{n\ge0}f^nA=X$. Let ...
6
votes
2answers
285 views

Entropy of nested compact invariant sets

Let $f$ be a homeomorphism on a compact metric space $X$. $K_1\supset K_2\supset\cdots \supset K$ are compact subsets of $X$ such that $f(K_n)=K_n$ and $K=\bigcap K_n$. If $h(f, K_1)<\infty$, do we ...
1
vote
0answers
88 views

Median entropy to observe evolution of system?

Hello, I am studying a dynamical system that takes as an initial condition a list. I want to analyze the evolution of Shannon's entropy in this system. I know the maximum entropy (50) and the minimum ...
0
votes
2answers
7k views

How to ensure the non-negativity of Kullback-Leibler Divergence KLD Metric (Relative Entropy)?

Hello, I’m having some problems in ensuring the non-negativity of KLD! I know that KLD is always positive and I went over the proof. However, it doesn’t seem to work for me. In some cases I’m ...
3
votes
2answers
1k views

Optimization of relative entropy

Wondering if my following question is an application of information theory: Lets say we have a factory and ship boxes of stuff outside. If a competitor stands outside my factory, observes the stream ...
4
votes
0answers
668 views

Entropy conjecture for flows

The entropy conjecture for diffeomorphisms (see for example this paper) asserts that for diffeomorphisms of manifolds, the log of the spectral radius of the actions of the diffeomorphism on the ...
1
vote
3answers
2k views

Entropy of Random Signal

How would you proof that for all equal variance (Continuous) Random Signals, a Gaussian one would have the largest Entropy. Or in other words, Given a Variance Gaussian PDF maximizes the Entropy. ...