  A system of globally coupled rotors is studied in a unified framework of
microcanonical and canonical ensembles. We consider the Fokker-Planck equation
governing the time evolution of the system, and examine various stationary as
well as non-stationary solutions. The canonical distribution, describing
equilibrium, provides a stationary solution also in the microcanonical
ensemble, which leads to order in a system with ferromagnetic coupling at low
temperatures. On the other hand, the microcanonical ensemble admits additional
stationary and non-stationary solutions; the latter allows dynamical order,
characterized by multiple degrees of clustering, for both ferromagnetic and
antiferromagnetic interactions. We present a detailed stability analysis of
these solutions: In a ferromagnetic system, the canonical distribution is
observed stable down to a certain temperature, which tends to get lower as the
number of Fourier components of the perturbed distribution is increased in the
analysis. The non-stationary solution remains neutrally stable below the
critical temperature, indicating inequivalence between the two ensembles. For
antiferromagnetic systems, all solutions are found to be neutrally stable at
all temperatures, suggesting that dynamical ordering is relatively easy to
observe at low temperatures compared with ferromagnetic systems.
