Flow of entropy in the evolution of the B^0 anti B^0 system: Upper bound on CP violation from unidirectionality

TL;DR

This paper explores the evolution of entropy in the B^0 anti B^0 system, establishing an upper bound on CP violation by analyzing the unidirectionality of entropy flow, which parallels previous bounds derived from the Stokes vector.

Contribution

It introduces an entropy-based measure to derive the same CP violation bound as previous methods, highlighting the physical implications of entropy flow in meson mixing.

Findings

Entropy flow unidirectionality yields the same CP violation bound as Stokes vector analysis.

Violation of the bound reveals specific physical features in the system.

Entropy-based approach provides an alternative perspective on CP violation constraints.

Abstract

We have previously studied the time-dependence of a B anti B meson mixture in terms of its density matrix. The requirement that the absolute value of the Stokes vector zeta(t) should evolve monotonically from its initial value zeta(0)=0 to its final value zeta(infinity)=1 was shown to lead to an upper bound on the CP violating overlap <B_L|B_S>. In the present note we consider an entropy variable S as an alternative measure of mixing. We show that exactly the same upper bound emerges from the requirement that the flow of entropy is unidirectional (dS/dt<0). We compare the entropic current dS/dt with and without CP violation and identify certain physical features that appear when the bound on <B_L|B_S> is violated.