  We study the evolution of a neutral $K$ meson prepared as an incoherent equal
mixture of $K^0$ and $\bar{K^0}$. Denoting the density matrix by $\rho(t) =
{1/2} N(t) [\1 + \vec{\zeta}(t) \cdot \vec{\sigma} ] $, the norm of the state
$N(t)$ is found to decrease monotonically from one to zero, while the magnitude
of the Stokes vector $|\vec{\zeta}(t)|$ increases monotonically from zero to
one. This property qualifies these observables as arrows of time. Requiring
monotonic behaviour of $N(t)$ for arbitrary values of $\gamma_L, \gamma_S$ and
$\Delta m$ yields a bound on the CP-violating overlap $\delta =
\braket{K_L}{K_S}$, which is similar to, but weaker than, the known unitarity
bound. A similar requirement on $|\vec{\zeta}(t)|$ yields a new bound,
$\delta^2 < {1/2} (\frac{\Delta \gamma}{\Delta m}) \sinh (\frac{3\pi}{4}
\frac{\Delta \gamma}{\Delta m})$ which is particularly effective in limiting
the CP-violating overlap in the $B^0$-$\bar{B^0}$ system. We obtain the Stokes
parameter $\zeta_3(t)$ which shows how the average strangeness of the beam
evolves from zero to $\delta$. The evolution of the Stokes vector from
$|\vec{\zeta}| = 0$ to $|\vec{\zeta}| = 1$ has a resemblance to an order
parameter of a system undergoing spontaneous symmetry breaking.
