  The goal of this note is to study limiting behavior of a self-organized
continuous flock evolving according to the 1D hydrodynamic Euler Alignment
model. We provide a series of quantitative estimates that show how far the
density of the limiting flock is from a uniform distribution. The key quantity
that controls density distortion is the entropy $\mathcal{H} = \int \rho \log
\rho \,\mbox{d}x$, and the measure of deviation from uniformity is given by a
well-known conserved quantity $e = u' + \mathcal{L}_\psi \rho$, where $u$ is
velocity and $\mathcal{L}_\psi $ is the communication operator with kernel
$\psi$. The cases of Lipschitz, singular geometric, and topological kernels are
covered in the study.
