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

We have proposed a novel way to specify the initial conditions of a dissipative fluid dynamical model for a given energy density $\varepsilon=u_μT^{μν}u_ν$ and baryon number density $n=N^μu_μ$, 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., $α\equiv μ/T$, $β\equiv1/T$ (where $T$ is separation temperature and $μ$ is separation chemical potential introduced to separate equilibrium part from the off-equilibrium state), a dissipative strength $γ$ is newly introduced to specify the off-equilibrium state. These $α$, $β$ and $γ$ can be uniquely determined by $\varepsilon$, $n$ and $P_{\rm eq}(α,β)+Π=-1/3Δ_{μν}T^{μν}$ consisting of both kinetic theoretical definitions and the thermodynamical stability condition. For $γ<10^{-3}$, $T$ and $μ$ are almost independent of $γ$, which means that the Landau matching condition is approximately satisfied. However, this is not the case for $γ\gtrsim 10^{-3}$.