Entropy density behavior poses many problems when we study non-equilibrium situations. In particular, the local equilibrium hypothesis (LEH) has played a very important role and is taken for granted in non-equilibrium problems, no matter how extreme they are. In this paper we would like to calculate the Boltzmann entropy balance equation for a plane shock wave and show its performance for Grad's 13-moment approximation and the Navier-Stokes-Fourier equations. In fact, we calculate the correction for the LEH in Grad's case and discuss its properties.
Keywords: entropy density; local equilibrium hypothesis; shock wave.