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arXiv · 1311.5667

A law of order estimation and leading-order terms for a family of averaged quantities on a multibaker chain system

Hideshi Ishida
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Abstract

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 $Δ$. 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 $Δ\rightarrow0$, and to confirm its partitioning independency. These deliverables fully explain the numerical results obtained by Ishida, consistent with the irreversible thermodynamics.

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Hideshi Ishida. 2014-05-28. A law of order estimation and leading-order terms for a family of averaged quantities on a multibaker chain system. https://doi.org/10.1063/1.4883397

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