The paper derives the hydrodynamics of perfect fluids that lack boost invariance directly from kinetic theory, building a Vlasov hierarchy on an axiomatically-constrained collision functional and, under a BGKW relaxation ansatz, obtaining a modified Euler equation with a drift term that relaxes the fluid toward co-moving equilibrium with its momentum reservoir. Its central result is an 'equation of kinetic state' — a parameterization of the velocity-dependent kinetic mass density — whose departure from the boost-invariant limit forces relations among the coefficients of the hydrodynamic derivative expansion, thereby recovering Toner-Tu active-flock hydrodynamics from microscopic symmetry and explaining why certain Toner-Tu coefficients are naturally of order one while others are naturally small.
We derive the hydrodynamic equations of perfect fluids without boost invariance [1] from kinetic theory. Our approach is to follow the standard derivation of the Vlasov hierarchy based on an a-priori…