Quantum entropy derived from first principles

TL;DR

This paper derives the fundamental properties of quantum entropy from first principles, showing that these properties uniquely determine its form and underpin all other characteristics of quantum entropy.

Contribution

It introduces a first-principles derivation of quantum entropy, establishing its unique form based on ensemble union properties.

Findings

Quantum entropy properties are derived from ensemble union principles.

The form of quantum entropy is uniquely determined up to normalization.

All other properties of quantum entropy follow from these fundamental principles.

Abstract

The most fundamental properties of quantum entropy are derived by considering the union of two ensembles. We discuss the limits these properties put on an entropy measure and obtain that they uniquely determine the form of the entropy functional up to normalisation. In particular, the result implies that all other properties of quantum entropy may be derived from these first principles.