“…For nonrelativistic velocities v/c ≪ 1, we have V ∝ 1/n ∝ m/ρ and E ∝ m v 2 /2 ∝ m/x. In fact, since the microcanonical description is more fundamental, definition (14), evaluated at the freeze out, is consistent with (3) and (13), and so it is also valid immediately after the freeze out era (once particle numbers are conserved). Since (14) is valid at both the initial and final states, respectively corresponding to the freeze out (s f , x f , n f ) and to the values associated with a suitable halo structure (s (h) , x (h) , n (h) ), the change in entropy per particle that follows from (14) between these two states is given by…”