Conformal symmetry and non-relativistic second-order fluid dynamics

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in the gradients of the hydrodynamic variables. At zeroth order, conformal symmetry implies a constraint on the equation of state, E0=23P, where E0E0 is the energy density and PP is the pressure. At first order, conformal symmetry implies that the bulk viscosity must vanish. We show that at second order, conformal invariance requires that two-derivative terms in the stress tensor must be traceless, and that it determines the relaxation of dissipative stresses to the Navier–Stokes form. We verify these results by solving the Boltzmann equation at second order in the gradient expansion. We find that only a subset of the terms allowed by conformal symmetry appear.

► We derive conformal constraints for the stress tensor of a scale invariant fluid.
► We determine the relaxation time in kinetic theory.
► We compute the rate of entropy production in second-order fluid dynamics.