Reasoning about quantum systems at the macroscopic level

TL;DR

This paper reviews the theoretical foundations of quantum statistical mechanics, focusing on generalized canonical distributions, quantum entropy, and the emergence of classical probability at the macroscopic scale.

Contribution

It provides an in-depth didactical analysis of quantum entropy, state reconstruction, and links between quantum and classical statistical mechanics.

Findings

Clarifies the role of generalized canonical distributions in quantum statistics

Details the definitions of quantum entropy and relative entropy

Explains how classical probability emerges from quantum systems

Abstract

In this didactical note I review in depth the rationale for using generalised canonical distributions in quantum statistics. Particular attention is paid to the proper definitions of quantum entropy and quantum relative entropy, as well as to quantum state reconstruction on the basis of incomplete data. There are two appendices in which I outline how generalised canonical distributions link to the conventional formulation of statistical mechanics, and how classical probability calculus emerges at the macroscopic level.