Year: 2024
Type: article
Abstract: All characterizations of the Shannon entropy include the so-called chain rule, a formula on a hierarchically structured probability distribution, which is based on at least two elementary distributions. We show that the chain rule can be split into two natural components, the well-known additivity of the entropy in case of cross-products and a variant of the chain rule that involves only a single elementary distribution. The latter is given as a proportionality relation and, hence, allows a vague interpretation as self-similarity, hence intrinsic property of the Shannon entropy. Analogous characterizations are given for the Rényi entropy and its limits, the min-entropy and the Hartley entropy.
Source: Entropy
DOI: 10.3390/e26121051
Authors: Martin Schlather, Carmen Ditscheid
Institution: University of Mannheim
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4405000751