On Entropy for general quantum systems

TL;DR

This paper provides a comprehensive framework for defining and characterizing entropy in classical and quantum systems, utilizing Orlicz space methods to unify various physical theories.

Contribution

It introduces a unified, rigorous approach to entropy applicable across classical, quantum, and quantum field systems using Orlicz space techniques.

Findings

Unified treatment of entropy in classical and quantum systems

Application of Orlicz spaces to large quantum systems

Framework applicable to quantum field theory

Abstract

In these notes we will give an overview and road map for a definition and characterization of (relative) entropy for both classical and quantum systems. In other words, we will provide a consistent treatment of entropy which can be applied within the recently developed Orlicz space based approach to large systems. This means that the proposed approach successfully provides a refined framework for the treatment of entropy in each of classical statistical physics, Dirac's formalism of Quantum Mechanics, large systems of quantum statistical physics, and finally also for Quantum Field Theory.