Modification of Eckart theory of relativistic dissipative fluid dynamics by introducing extended matching conditions

We deal with a novel approach to formulation of the relativistic dissipative hydrodynamics by extending the so-called matching conditions widely used in the literature. The form of the nonequilibrium entropy current can be determined by requiring thermodynamical stability of the entropy current under extended matching conditions. We derive equations of motion for the relativistic dissipative fluid based on the Eckart theory and show that linearized equations obtained from them are stable against small perturbations. It is also shown that the required fluid stability conditions are related to the causality of the model.