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Xu, YZ; Yeung, CH; Zhou, HJ; Saad, D2
Entropy Inflection and Invisible Low-Energy States: Defensive Alliance Example
Source PublicationPHYSICAL REVIEW LETTERS
Language英语
KeywordSTATISTICAL-MECHANICS TREES MODEL
AbstractLower 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.
2018
ISSN0031-9007
Volume121Issue:21Pages:210602
Cooperation Status国际
Subject AreaPhysics
MOST Discipline CataloguePhysics, Multidisciplinary
Indexed BySCIE
Funding OrganizationLeverhulme 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]
Document Type期刊论文
Identifierhttp://ir.itp.ac.cn/handle/311006/22753
Collection计算平台成果
Affiliation1.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
Recommended Citation
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.
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