Maximum Entropy Principle in statistical inference: case for non-Shannonian entropies

TL;DR

This paper broadens the scope of the Maximum Entropy Principle by showing it applies to a wider class of entropies beyond Shannon's, supported by examples from quantum and nuclear physics.

Contribution

It demonstrates that Shore--Johnson axioms encompass non-Shannonian entropies, expanding the theoretical foundation of statistical inference.

Findings

Shore--Johnson axioms apply to a wider class of entropies.

Analysis of weak correlations in quantum and nuclear systems.

Examples include 2-qubit quantum systems and strongly interacting nuclear systems.

Abstract

In this letter we show that the Shore--Johnson axioms for Maximum Entropy Principle in statistical estimation theory account for a considerably wider class of entropic functional than previously thought. Apart from a formal side of the proof, we substantiate our point by analyzing the effect of weak correlations and discuss two pertinent examples: $2$-qubit quantum system and strongly interacting nuclear systems.