We present a new formalism for the theory of relativistic dissipative hydrodynamics, where covariance and causality are satisfied by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

We consider the modification of the Cahn-Hilliard equation when a time delay process through a memory function is taken into account. We then study the process of spinodal decomposition in fast phase transitions associated with a conserved order parameter. The introduced memory effect plays an important role to obtain a finite group velocity. Then, we discuss the constraint for the parameters to satisfy causality. The memory effect is seen to affect the dynamics of phase transition at short times and have the effect of delaying, in a significant way, the process of rapid growth of the order parameter that follows a quench into the spinodal region.

We discuss the minimal structure of relativistic dissipative hydrodynamics which satisfies the covariance and causality by introducing the memory effect in irreversible currents.

Some consequences of the presence of critical point in the equation of state on the hydrodynamical evolution of the strongly interacting matter are discussed. For this purpose, we apply the low energy effective theory of QCD, the Nambu-Jona-Lasinio model and show some examples.

We present a new formalism for the relativistic dissipative hydrodynamics consistent with causality. We start from the physical analysis of the irreversible currents according to the Landau-Lifshitz theory. Then, the irreversible currents are given by integral expressions which take into account the relaxation time. Only one additional parameter was introduced, the relaxation time, tauR. We verified that the linearized equation of motion for small perturbations in the homogeneous, static background coincides with Hiscock-Lindblom.