Ishida H.,3 Machikaneyama
Journal of Mathematical Physics | Year: 2014
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 in the bulk system is proved, making it possible to estimate the order of the quantities with respect to the representative partition scale parameter Δ. 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 Δ → 0, and to confirm its partitioning independency. These deliverables fully explain the numerical results obtained by Ishida, consistent with the irreversible thermodynamics. © 2014 AIP Publishing LLC.