Entropy, subentropy and the elementary symmetric functions

2013/10/24 by Richard Jozsa, Jozsa, Richard, Graeme Mitchison +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Statistical Methods and Models #FOS: Physical sciences #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Quantum Physics (quant-ph) #Statistical Mechanics and Entropy #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.1310.6629

arxiv created 2013/10/24 · openalex publication_date 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use complex contour integral techniques to study the entropy H and subentropy Q as functions of the elementary symmetric polynomials, revealing a series of striking properties. In particular for these variables, derivatives of -Q are equal to derivatives of H of one higher order and the first derivatives of H and Q are seen to be completely monotone functions. It then follows that exp (-H) and exp(-Q) are Laplace transforms of infinitely divisible probability distributions.

Cited by

• Vector rearrangement invariant banach spaces of random variables with exponential decreasing tails of distributions
• Symmetric polynomials in information theory: entropy and subentropy

Related

• Symmetric polynomials in information theory: entropy and subentropy
• A notion of entropy on the roots of polynomials
• Superresolution in the maximum entropy approach to invert Laplace transforms
• Derivatives of entropy and the MMSE conjecture
• The Entropy Influence Conjecture Revisited