RG/E Derivation of Relativistic Second-Order Fluid Dynamics

We derive the relativistic second-order fluid dynamic equation and the microscopic formulae of the relaxation times as well as the transport coefficients systematically from the relativistic Boltzmann equation with quantum statistics. The derivation is based on the doublet scheme in the RG method introduced in Chap. 9 as a general framework to extract the mesoscopic dynamics from the underlying microscopic theory. The resultant relativistic second-order fluid dynamic equation is uniquely defined in the energy frame and the microscopic representations of the transport coefficients are of the same forms as those given by the Chapman-Enskog expansion method, both in accordance with the first-order one presented in Chap. 11 . We show that the microscopic expressions of the relaxation times have natural and physically plausible forms. We prove that the derived fluid dynamic equation is not only stable but also causal.