Two extensions of exact nonequilibrium steady states of a boundary-driven cellular automaton
Two extensions of exact nonequilibrium steady states of a boundary-driven cellular automaton
复制标题
边界驱动元胞自动机的精确非平衡稳态的两种扩展
DOI：
10.1088/1751-8121/aadc29
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发表时间：
2018
期刊：
影响因子：
--
通讯作者：
S. Takesue
中科院分区：
文献类型：
--
作者：
A. Inoue;S. Takesue
最近，Prosen和Mejía-Mondello（2016 J. Phys. A：Math. Theor. 49 185003）得到了一类可积可逆元胞自动机在随机边界条件驱动下的精确非平衡定态.在本文中，我们探讨了可能的扩展，他们的方法通过推广的边界条件。因此，我们发现两种情况下，这样的扩展是可能的。一个是通过概括的概率值的虚拟细胞，同时施加一个特殊的条件上的发射和吸收率。虽然这实际上与Prosen和Buča（2017 J. Phys. A：Math. Theor. 50 395002），我们提出了一种不同形式的解决方案。另一种是通过将守恒量视为能量，并将边界视为热源而获得的。后者包含原始解和作为特例的前一个。这两种解决方案的性质进行了讨论。
Recently Prosen and Mejía-Monasterio (2016 J. Phys. A: Math. Theor. 49 185003) obtained exact nonequilibrium steady states of an integrable and reversible cellular automaton driven by some stochastic boundary conditions. In this paper, we explore the possible extensions of their method by generalizing the boundary conditions. As the result, we find two cases where such an extension is possible. One is obtained by generalizing probabilities for values of virtual cells while imposing a special condition on emission and absorption rates. Although this actually coincides with the conditional boundary driving discussed in Prosen and Buča (2017 J. Phys. A: Math. Theor. 50 395002), we present a solution in a different form. The other is obtained by considering a conserved quantity as energy, and by considering boundaries as heat reservoirs. The latter contains the original solution and the former one as the special cases. Properties of both solutions are discussed.