Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example

	Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
	Xu, YZ ; Yeung, CH ; Zhou, HJ; Saad, D 2
刊名	PHYSICAL REVIEW LETTERS
	2018
卷号	121 期号:21 页码:210602
关键词	STATISTICAL-MECHANICS TREES MODEL
ISSN号	0031-9007
英文摘要	Lower temperature leads to a higher probability of visiting low-energy states. This intuitive belief underlies most physics-inspired strategies for addressing hard optimization problems. For instance, the popular simulated annealing (SA) dynamics is expected to approach a ground state if the temperature is lowered appropriately. Here, we demonstrate that this belief is not always justified. Specifically, we employ the cavity method to analyze the minimum strong defensive alliance problem and discover a bifurcation in the solution space, induced by an inflection point in the entropy-energy profile. While easily accessible configurations are associated with the lower-free-energy branch, the low-energy configurations are associated with the higher-free-energy branch within the same temperature range. There is a discontinuous phase transition between the high-energy configurations and the ground states, which generally cannot be followed by SA. We introduce an energy-clamping strategy to obtain superior solutions by following the higher-free-energy branch, overcoming the limitations of SA.
学科主题	Physics
语种	英语
资助机构	Leverhulme Trust [RPG-2013-48] ; Research Grants Council of Hong Kong [18304316, 18301217] ; National Natural Science Foundation of China [11421063, 11747601] ; Chinese Academy of Sciences [QYZDJ-SSW-SYS018]
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/22753]
专题	计算平台成果
作者单位	1.Chinese Acad Sci, Inst Theoret Phys, CAS Key Lab Theoret Phys, Beijing 100190, Peoples R China 2.Educ Univ Hong Kong, Dept Sci & Environm Studies, Hong Kong, Hong Kong, Peoples R China 3.Aston Univ, Nonlinear & Complex Res Grp, Birmingham B4 7ET, W Midlands, England 4.Univ Chinese Acad Sci, Sch Phys Sci, Beijing 100049, Peoples R China 5.Hunan Normal Univ, Synerget Innovat Ctr Quantum Effects & Applicat, Changsha 410081, Hunan, Peoples R China
推荐引用方式 GB/T 7714	Xu, YZ,Yeung, CH,Zhou, HJ,et al. Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example[J]. PHYSICAL REVIEW LETTERS,2018,121(21):210602.
APA	Xu, YZ,Yeung, CH,Zhou, HJ,&Saad, D.(2018).Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example.PHYSICAL REVIEW LETTERS,121(21),210602.
MLA	Xu, YZ,et al."Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example".PHYSICAL REVIEW LETTERS 121.21(2018):210602.