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Entropy 2008, 10(4), 765-775; doi:10.3390/e10040765
Article

Non-linear Information Inequalities

*  and
Received: 24 May 2008 / Accepted: 9 December 2008 / Published: 22 December 2008
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Abstract

We construct non-linear information inequalities from Mat´uˇs’ infinite series of linear information inequalities. Each single non-linear inequality is sufficiently strong to prove that the closure of the set of all entropy functions is not polyhedral for four or more random variables, a fact that was already established using the series of linear inequalities. To the best of our knowledge, they are the first non-trivial examples of non-linear information inequalities.
Keywords: Entropy; entropy function; nonlinear information inequality; nonshannon type information inequality Entropy; entropy function; nonlinear information inequality; nonshannon type information inequality
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Chan, T.; Grant, A. Non-linear Information Inequalities. Entropy 2008, 10, 765-775.

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