  It has been recently shown that any halo velocity bias present in the initial
conditions does not decay to unity, in agreement with predictions from peak
theory. However, this is at odds with the standard formalism based on the
coupled fluids approximation for the coevolution of dark matter and halos.
Starting from conservation laws in phase space, we discuss why the fluid
momentum conservation equation for the biased tracers needs to be modified in
accordance with the change advocated in Baldauf, Desjacques & Seljak (2014).
Our findings indicate that a correct description of the halo properties should
properly take into account peak constraints when starting from the
Vlasov-Boltzmann equation.
