  We investigate the entropy production within dissipative hydrodynamics in the
Israel-Stewart (IS) and Navier-Stokes theory (NS) for relativistic heavy ion
physics applications. In particular we focus on the initial condition in a 0+1D
Bjorken scenario, appropriate for the early longitudinal expansion stage of the
collision. Going beyond the standard simplification of a massless ideal gas we
consider a realistic equation of state consistently derived within a virial
expansion. The EoS used is well in line with recent three-flavor QCD lattice
data for the pressure, speed of sound, and interaction measure at nonzero
temperature and vanishing chemical potential ($\mu_{\rm q} = 0$). The shear
viscosity has been consistently calculated within this formalism using a
kinetic approach in the ultra-relativistic regime with an explicit and
systematic evaluation of the transport cross section as function of
temperature. We investigate the influence of the viscosity and the initial
condition, i.e. formation time, initial temperature, and pressure anisotropy
for the entropy production at RHIC at $\sqrt{s_{\rm NN}}=130$ GeV. We find that
the interplay between effects of the viscosity and of the realistic EoS can not
be neglected in the reconstruction of the initial state from experimental data.
Therefore, from the experimental findings it is very hard to derive unambiguous
information about the initial conditions and/or the evolution of the system.
