Separation of equilibrium part from an off-equilibrium state produced by relativistic heavy ion collisions using a scalar dissipative strength

Abstract

We have proposed a novel way to specify the initial conditions of a dissipative fluid dynamical model for a given energy density $\varepsilon=u_{\mu}T^{\mu\nu}u_{\nu}$ and baryon number density $n=N^{\mu}u_{\mu}$, which does not impose the so-called Landau matching condition for an off-equilibrium state. In addition to usual two parameters for equilibrium part, i.e., $\alpha\equiv \mu/T$, $\beta\equiv1/T$ (where $T$ is separation temperature and $\mu$ is separation chemical potential introduced to separate equilibrium part from the off-equilibrium state), a dissipative strength $\gamma$ is newly introduced to specify the off-equilibrium state. These $\alpha$, $\beta$ and $\gamma$ can be uniquely determined by $\varepsilon$, $n$ and $P_{\rm eq}(\alpha,\beta)+\Pi=-1/3\Delta_{\mu\nu}T^{\mu\nu}$ consisting of both kinetic theoretical definitions and the thermodynamical stability condition. For $\gamma <10^{-3}$, $T$ and $\mu$ are almost independent of $\gamma$, which means that the Landau matching condition is approximately satisfied. However, this is not the case for $\gamma \gtrsim 10^{-3}$.