  We use the entropy method to analyze the nonlinear dynamics and stability of
a continuum kinetic model of an active nematic suspension. From the time
evolution of the relative entropy -- an energy-like quantity in the kinetic
model -- we derive a variational bound on relative entropy fluctuations that
can be expressed in terms of orientational order parameters. From this bound we
show isotropic suspensions are nonlinearly stable for sufficiently low
activity, and derive upper bounds on spatiotemporal averages in the unstable
regime that are consistent with fully nonlinear simulations. This work
highlights the self-organizing role of activity in particle suspensions, and
places limits on how organized such systems can be.
