  We give a modified derivation of the Einstein equation of state by
considering the Clausius relation $T\delta S-\delta N =\delta Q$ on a null
hypersurface with a non-vanishing expansion ($\theta \neq 0$), i.e. not in the
equilibrium. The derivation corresponds to choosing a specific observer to the
hypersurface, and such a generalization gives a hint how we can improve the
original derivation by Jacobson. We also give an interpretation of the
thermodynamic relation based on the Noether charge method.
