The Cabibbo-Kobayashi-Maskawa density matrices

TL;DR

This paper analyzes the properties of density matrices derived from the CKM matrix in the Standard Model, showing that weak interaction-induced quark mixtures do not increase entropy and are unrelated to thermodynamic entropy changes.

Contribution

It introduces a quantum statistical framework for CKM matrix-induced quark states and proves their entropy remains unchanged due to unitarity, linking symmetry violations to quantum coherence.

Findings

Density matrices for quark families are defined and analyzed.

Unitarity of CKM matrix ensures no entropy increase in quark mixtures.

CP and T violation are shown to be unrelated to entropy changes.

Abstract

The flavor changing charged currents of the weak sector of the Standard Model are studied in the framework of a quantum statistical approach. The quantum superposition of same-type quarks, generated by the Cabibbo-Kobayashi-Maskawa matrix, is used to define three density matrices, one for each quark family. The properties of such density matrices are analyzed, in particular, the associated von Neumann entropy. It is proven that, due to the unitarity of the Cabibbo-Kobayashi-Maskawa matrix, the quantum mixtures of quarks resulting from the weak interaction do not increase entropy and, therefore, the violation of CP and T symmetries cannot be related to the second law of thermodynamics.