  We introduce a system of self-propelled agents (active Brownian particles)
with velocity alignment in two spatial dimensions and derive a mean-field
theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and
a moment expansion of the probability distribution function. We analyze the
stationary solutions corresponding to macroscopic collective motion with finite
center of mass velocity (ordered state) and the disordered solution with no
collective motion in the spatially homogeneous system. In particular, we
discuss the impact of two different propulsion functions governing the
individual dynamics. Our results predict a strong impact of the individual
dynamics on the mean field onset of collective motion (continuous vs
discontinuous). In addition to the macroscopic density and velocity field we
consider explicitly the dynamics of an effective temperature of the agent
system, representing a measure of velocity fluctuations around the mean
velocity. We show that the temperature decreases strongly with increasing level
of collective motion despite constant fluctuations on individual level, which
suggests that extreme caution should be taken in deducing individual behavior,
such as, state-dependent individual fluctuations from mean-field measurements
[Yates {\em et al.}, PNAS, 106 (14), 2009].

Statistical Mechanics;Other Quantitative Biology