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.

翻译：基于香农熵的经典最大熵原理被广泛用于从部分信息构建最小偏倚概率分布。然而，唯一确定香农泛函的肖尔-约翰逊公理依赖于强系统独立性假设，这一假设在现实世界中强相关系统中常被违反。本文为实践者提供了一个自包含的指南，说明何时及为何应放弃香农熵形式，转而采用单参数的乌芬克-吉兹巴-科贝尔广义熵族。在从应用视角回顾肖尔-约翰逊公理后，我们梳理了最常用的熵泛函，并将其定位在UJK族中。通过经济学和生态学两个应用案例，明确阐释了广义熵的必要性。一个详细演算的简单数学模型展示了广义最大熵方法在处理强系统独立性不成立情况时的优势。最后，我们提供了选择熵度量及报告结果的实用指南，以确保分析保持透明性和可复现性。