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We deal with a novel approach to formulation of the relativistic dissipativehydrodynamics by extending the so-called matching conditions widely used in theliterature. The form of the non-equilibrium entropy current can be determinedby requiring thermodynamical stability of the entropy current under extendedmatching conditions. We derive equations of motion for the relativisticdissipative fluid based on the Eckart theory and show that linearized equationsobtained from them are stable against small perturbations. It is also shownthat the required fluid stability conditions are related to the causality ofthe model.

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