Characterizing Entropy in Statistical Physics and in Quantum Information Theory

TL;DR

This paper presents an axiomatic framework for entropy in quantum mechanics, deriving key formulas like Boltzmann-Planck and von Neumann from minimal assumptions, clarifying foundational principles.

Contribution

It introduces a new axiomatic characterization of quantum entropy, replacing unspoken assumptions with proven consequences and deriving fundamental formulas from basic principles.

Findings

Derivation of the Boltzmann-Planck formula from axioms

Deduction of the von Neumann entropy formula using probability theory

Unveiling and replacing traditional unspoken assumptions in entropy foundations

Abstract

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann-Planck formula is derived. Building on this formula, using the Law of Large Numbers - a basic theorem of probability theory - the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.