Tags

Type your tag names separated by a space and hit enter

Entropy Governed by the Absorbing State of Directed Percolation.
Phys Rev Lett 2019; 123(9):090601PR

Abstract

We investigate the informational aspect of (1+1)-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.

Authors+Show Affiliations

Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan.Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581, Japan.

Pub Type(s)

Journal Article

Language

eng

PubMed ID

31524449

Citation

Harada, Kenji, and Naoki Kawashima. "Entropy Governed By the Absorbing State of Directed Percolation." Physical Review Letters, vol. 123, no. 9, 2019, p. 090601.
Harada K, Kawashima N. Entropy Governed by the Absorbing State of Directed Percolation. Phys Rev Lett. 2019;123(9):090601.
Harada, K., & Kawashima, N. (2019). Entropy Governed by the Absorbing State of Directed Percolation. Physical Review Letters, 123(9), p. 090601. doi:10.1103/PhysRevLett.123.090601.
Harada K, Kawashima N. Entropy Governed By the Absorbing State of Directed Percolation. Phys Rev Lett. 2019 Aug 30;123(9):090601. PubMed PMID: 31524449.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Entropy Governed by the Absorbing State of Directed Percolation. AU - Harada,Kenji, AU - Kawashima,Naoki, PY - 2019/06/13/revised PY - 2019/04/08/received PY - 2019/9/17/entrez PY - 2019/9/17/pubmed PY - 2019/9/17/medline SP - 090601 EP - 090601 JF - Physical review letters JO - Phys. Rev. Lett. VL - 123 IS - 9 N2 - We investigate the informational aspect of (1+1)-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. SN - 1079-7114 UR - https://www.unboundmedicine.com/medline/citation/31524449/Entropy_Governed_by_the_Absorbing_State_of_Directed_Percolation L2 - http://link.aps.org/abstract/PRL/v123/p090601 DB - PRIME DP - Unbound Medicine ER -