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We use the entropy method to analyze the nonlinear dynamics and stability ofa continuum kinetic model of an active nematic suspension. From the timeevolution of the relative entropy -- an energy-like quantity in the kineticmodel -- we derive a variational bound on relative entropy fluctuations thatcan be expressed in terms of orientational order parameters. From this bound weshow isotropic suspensions are nonlinearly stable for sufficiently lowactivity, and derive upper bounds on spatiotemporal averages in the unstableregime that are consistent with fully nonlinear simulations. This workhighlights the self-organizing role of activity in particle suspensions, andplaces limits on how organized such systems can be.

Variational bounds and nonlinear stability of an active nematic suspension