Entropy Governed by the Absorbing State of Directed Percolation
Entropy Governed by the Absorbing State of Directed Percolation
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熵由定向渗透的吸收状态控制
DOI：
10.1103/physrevlett.123.090601
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发表时间：
2019
影响因子：
8.6
通讯作者：
Kawashima Naoki
中科院分区：
文献类型：
--
作者：
Harada Kenji;Kawashima Naoki
我们研究了()维定向渗流的信息方面，这是一个非平衡连续相变的正则模型，它由一个被称为“吸收”态的单一特殊状态主导。利用张量网络格式，数值计算了定向渗流的状态概率分布随时间的演化。我们在吸收相变点上发现了Rényi熵的普适松弛，并在活性相中发现了一个新的奇点，该奇点略有但明显地远离吸收相变点。在新的奇点，二阶Rényi熵有一个明确的尖点。在那里，我们还检测到了“纠缠熵”的奇异行为，通过将概率分布视为波函数来定义。纠缠熵在奇点以下消失，在奇点上方保持有限。我们确认，虽然吸收态在活跃期出现的次数很少，但它是造成这些现象的原因。这一解释使我们对临界点和活跃期的Rényi熵的时间演化有了统一的认识。
We investigate the informational aspect of ()-dimensional directed percolation, a canonical model of a nonequilibrium continuous transition to a phase dominated by a single special state called the “absorbing” state. Using a tensor network scheme, we numerically calculate the time evolution of state probability distribution of directed percolation. We find a universal relaxation of Rényi entropy at the absorbing phase transition point as well as a new singularity in the active phase, slightly but distinctly away from the absorbing transition point. At the new singular point, the second-order Rényi entropy has a clear cusp. There we also detect a singular behavior of “entanglement entropy,” defined by regarding the probability distribution as a wave function. The entanglement entropy vanishes below the singular point and stays finite above. We confirm that the absorbing state, though its occurrence is exponentially rare in the active phase, is responsible for these phenomena. This interpretation provides us with a unified understanding of time evolution of the Rényi entropy at the critical point as well as in the active phase.