2023•EntropyOpen access

On the Entropy and the Maximum Entropy Principle of Uncertain Variables

Yujun Liu, Guanzhong Ma

Abstract

A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler-Lagrange equation.

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Key concepts: Maximum entropy thermodynamics, Mathematics, Principle of maximum entropy, Statistical physics, Entropy (arrow of time), Maximum entropy probability distribution, Min entropy, Joint quantum entropy