  Self-propelled particle (SPP) systems are intrinsically out of equilibrium
systems, where each individual particle converts energy into work to move in a
dissipative medium. When interacting through a velocity alignment mechanism,
and the medium acts as a momentum sink, even momentum is not conserved. In this
scenario, a mapping into an equilibrium system seems unlikely. Here, we show
that an entropy functional can be derived for SPPs with velocity alignment and
density-dependent speed, at least in the (orientationally) disordered phase.
This non-trivial result has important physical consequences. The study of the
entropy functional reveals that the system can undergo phase separation before
the orientational-order phase transition known to occur in SPP systems with
velocity alignment.Moreover, we indicate that the spinodal line is a function
of the alignment sensitivity and show that density fluctuations as well as the
critical spatial diffusion, that leads to phase separation, dramatically
increase as the orientational-order transition is approached.
