  We prove that the geodesic flow on a compact locally CAT(-1) space has the
weak specification property, and give various applications. We show that every
H\"older potential on the space of geodesics has a unique equilibrium state. We
establish the equidistribution of weighted periodic orbits and the large
deviations principle for all such measures. The thermodynamic results are
proved for the class of expansive flows with weak specification.
