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

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.