The Constraints Determining Forms of Entropy and Inducing Equilibrium Distributions

TL;DR

This paper introduces a framework for understanding how constraints influence the forms of entropy and the resulting equilibrium distributions, supported by axioms and theorems.

Contribution

It presents a new constraint-based approach with formal axioms and theorems to analyze entropy forms and equilibrium distributions.

Findings

Established axioms for constraint-based statistics

Proved six theorems linking constraints to entropy forms

Provided a theoretical foundation for entropy and equilibrium analysis

Abstract

The ideas of the constraint-based statistics are introduced. The axiom and six theorems of the constraint-based statistics are established.