Entropic Trends in Information Theory

The field of information theory is witnessing a significant shift towards the development of new entropic functionals and the exploration of their properties. Recent research has focused on the study of entropies associated with orbits of finite groups, leading to the discovery of new relationships between entropies and the cardinalities of orbits. The use of information-theoretic tools to analyze and quantify the stability of inequalities, such as the Ingleton inequality, has also gained attention. Furthermore, advancements in the field have led to the strengthening of existing inequalities, including Han's Fourier entropy-influence inequality. Notably, the behavior of maximal leakage over Bayesian networks is being investigated, with new bounds and characterizations being established. Some noteworthy papers in this area include: the study on entropies associated with orbits of finite groups, which introduces new entropic functionals linked to Dynkin diagrams. The paper on strengthening Han's Fourier entropy-influence inequality provides a short information-theoretic proof that establishes the inequality as an elementary structural property of Shannon entropy and influence.

Sources

Entropies associated with orbits of finite groups

Structural Properties of Entropic Vectors and Stability of the Ingleton Inequality

Strengthening Han's Fourier Entropy-Influence Inequality via an Information-Theoretic Proof

Bounds on Maximal Leakage over Bayesian Networks

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