  In this study a family of local quantities defined on each partition and its
averaging on a macroscopic small region, site, are defined on a multibaker
chain system. On its averaged quantities, a law of order estimation (LOE) in
the bulk system is proved, making it possible to estimate the order of the
quantities with respect to the representative partition scale parameter
$\Delta$. Moreover, the form of the leading-order terms of the averaged
quantities is obtained, and the form enables us to have the macroscopic
quantity in the continuum limit, as $\Delta\rightarrow0$, and to confirm its
partitioning independency. These deliverables fully explain the numerical
results obtained by Ishida, consistent with the irreversible thermodynamics.
