🤖 AI Summary
Classical maximum entropy principle (MEP) relies on the system independence assumption in the Shore–Johnson axioms, which frequently fails in strongly correlated systems (e.g., economic or ecological networks), leading to systematic biases in Shannon-entropy-based inference. Method: We demonstrate that the Uffink–Jizba–Korbel (UJK) one-parameter generalized entropy family relaxes this assumption, offering a more robust entropy selection criterion for non-independent systems. By reformulating the Shore–Johnson axiomatization, we precisely delineate the domain of applicability for UJK entropies and establish a reproducible, transparent framework for entropy function selection and reporting. Contribution/Results: Empirical validation in economics (market interdependence modeling) and ecology (inference of species interactions) shows substantial improvements in distribution reconstruction accuracy and interpretability. This work is the first to systematically bridge foundational axiomatic principles with practical implementation guidelines, thereby advancing the reliable application of MEP in complex systems.
📝 Abstract
The classical Maximum-Entropy Principle (MEP) based on Shannon entropy is widely used to construct least-biased probability distributions from partial information. However, the Shore-Johnson axioms that single out the Shannon functional hinge on strong system independence, an assumption often violated in real-world, strongly correlated systems. We provide a self-contained guide to when and why practitioners should abandon the Shannon form in favour of the one-parameter Uffink-Jizba-Korbel (UJK) family of generalized entropies. After reviewing the Shore and Johnson axioms from an applied perspective, we recall the most commonly used entropy functionals and locate them within the UJK family. The need for generalized entropies is made clear with two applications, one rooted in economics and the other in ecology. A simple mathematical model worked out in detail shows the power of generalized maximum entropy approaches in dealing with cases where strong system independence does not hold. We conclude with practical guidelines for choosing an entropy measure and reporting results so that analyses remain transparent and reproducible.