Application of density functional theory to relativistic hydrodynamics

Abstract

The density functional method is used in nonrelativistic hydrodynamics for a description of multicomponent multiphase mixtures. The method is based on an expression for the entropy in the form of a functional with terms quadratic in gradients of component densities. In the present work, the density functional theory is generalized to the relativistic case. This generalization involves a solution of a number of problems: relativistically covariant formulation of the theory equations, derivation of basic relationships with allowance for the generalized relativistic principle of entropy production, and check of the relativistic causality of the theory. It is demonstrated that higher-order derivatives in the theory appear to be compatible with the causality in the basic relationships nonlocal in space and time.