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TOPICAL REVIEW — Statistical Physics and Complex Systems
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Collective behaviors of suprachiasm nucleus neurons under different light-dark cycles
Gu Chang-Gui (顾长贵), Zhang Xin-Hua (张新华), Liu Zong-Hua (刘宗华)
Chin. Phys. B, 2014, 23 (
7
): 078702. DOI:
10.1088/1674-1056/23/7/078702
Abstract
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553
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461
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The principal circadian clock in the suprachiasm nucleus (SCN) regulates the circadian rhythm of physiological and behavioral activities of mammals. Except for the normal function of the circadian rhythm, the ensemble of SCN neurons may show two collective behaviors, i.e., a free running period in the absence of a light-dark cycle and an entrainment ability to an external
T
cycle. Experiments show that both the free running periods and the entrainment ranges may vary from one species to another and can be seriously influenced by the coupling among the SCN neurons. We here review the recent progress on how the heterogeneous couplings influence these two collective behaviors. We will show that in the case of homogeneous coupling, the free running period increases monotonically while the entrainment range decreases monotonically with the increase of the coupling strength. While in the case of heterogenous coupling, the dispersion of the coupling strength plays a crucial role. It has been found that the free running period decreases with the increase of the dispersion while the entrainment ability is enhanced by the dispersion. These findings provide new insights into the mechanism of the circadian clock in the SCN.
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Nonequilibrium thermodynamics and fluctuation relations for small systems
Cao Liang (曹亮), Ke Pu (柯谱), Qiao Li-Yan (乔丽颜), Zheng Zhi-Gang (郑志刚)
Chin. Phys. B, 2014, 23 (
7
): 070501. DOI:
10.1088/1674-1056/23/7/070501
Abstract
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678
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1158
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In this review, we give a retrospect of the recent progress in nonequilibrium statistical mechanics and thermodynamics in small dynamical systems. For systems with only a few number of particles, fluctuations and nonlinearity become significant and contribute to the nonequilibrium behaviors of the systems, hence the statistical properties and thermodynamics should be carefully studied. We review recent developments of this topic by starting from the Gallavotti-Cohen fluctuation theorem, and then to the Evans-Searles transient fluctuation theorem, Jarzynski free-energy equality, and the Crooks fluctuation relation. We also investigate the nonequilibrium free energy theorem for trajectories involving changes of the heat bath temperature and propose a generalized free-energy relation. It should be noticed that the non-Markovian property of the heat bath may lead to the violation of the free-energy relation.
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Percolation on networks with dependence links
Li Ming (李明), Wang Bing-Hong (汪秉宏)
Chin. Phys. B, 2014, 23 (
7
): 076402. DOI:
10.1088/1674-1056/23/7/076402
Abstract
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576
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As a classical model of statistical physics, the percolation theory provides a powerful approach to analyze the network structure and dynamics. Recently, to model the relations among interacting agents beyond the connection of the networked system, the concept of dependence link is proposed to represent the dependence relationship of agents. These studies suggest that the percolation properties of these networks differ greatly from those of the ordinary networks. In particular, unlike the well known continuous transition on the ordinary networks, the percolation transitions on these networks are discontinuous. Moreover, these networks are more fragile for a broader degree distribution, which is opposite to the famous results for the ordinary networks. In this article, we give a summary of the theoretical approaches to study the percolation process on networks with inter- and inner-dependence links, and review the recent advances in this field, focusing on the topology and robustness of such networks.
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RNA structure prediction:Progress and perspective
Shi Ya-Zhou (时亚洲), Wu Yuan-Yan (吴园燕), Wang Feng-Hua (王凤华), Tan Zhi-Jie (谭志杰)
Chin. Phys. B, 2014, 23 (
7
): 078701. DOI:
10.1088/1674-1056/23/7/078701
Abstract
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933
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Many recent exciting discoveries have revealed the versatility of RNAs and their importance in a variety of cellular functions which are strongly coupled to RNA structures. To understand the functions of RNAs, some structure prediction models have been developed in recent years. In this review, the progress in computational models for RNA structure prediction is introduced and the distinguishing features of many outstanding algorithms are discussed, emphasizing three-dimensional (3D) structure prediction. A promising coarse-grained model for predicting RNA 3D structure, stability and salt effect is also introduced briefly. Finally, we discuss the major challenges in the RNA 3D structure modeling.
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Statistical physics of hard combinatorial optimization:Vertex cover problem
Zhao Jin-Hua (赵金华), Zhou Hai-Jun (周海军)
Chin. Phys. B, 2014, 23 (
7
): 078901. DOI:
10.1088/1674-1056/23/7/078901
Abstract
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538
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537
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Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.
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Statistical physics of human beings in games:Controlled experiments
Liang Yuan (梁源), Huang Ji-Ping (黄吉平)
Chin. Phys. B, 2014, 23 (
7
): 078902. DOI:
10.1088/1674-1056/23/7/078902
Abstract
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643
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986
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It is important to know whether the laws or phenomena in statistical physics for natural systems with non-adaptive agents still hold for social human systems with adaptive agents, because this implies whether it is possible to study or understand social human systems by using statistical physics originating from natural systems. For this purpose, we review the role of human adaptability in four kinds of specific human behaviors, namely, normal behavior, herd behavior, contrarian behavior, and hedge behavior. The approach is based on controlled experiments in the framework of market-directed resource-allocation games. The role of the controlled experiments could be at least two-fold: adopting the real human decision-making process so that the system under consideration could reflect the performance of genuine human beings; making it possible to obtain macroscopic physical properties of a human system by tuning a particular factor of the system, thus directly revealing cause and effect. As a result, both computer simulations and theoretical analyses help to show a few counterparts of some laws or phenomena in statistical physics for social human systems: two-phase phenomena or phase transitions, entropy-related phenomena, and a non-equilibrium steady state. This review highlights the role of human adaptability in these counterparts, and makes it possible to study or understand some particular social human systems by means of statistical physics coming from natural systems.
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A mini-review on econophysics:Comparative study of Chinese and western financial markets
Zheng Bo (郑波), Jiang Xiong-Fei (蒋雄飞), Ni Peng-Yun (倪鹏云)
Chin. Phys. B, 2014, 23 (
7
): 078903. DOI:
10.1088/1674-1056/23/7/078903
Abstract
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684
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642
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We present a review of our recent research in econophysics, and focus on the comparative study of Chinese and western financial markets. By virtue of concepts and methods in statistical physics, we investigate the time correlations and spatial structure of financial markets based on empirical high-frequency data. We discover that the Chinese stock market shares common basic properties with the western stock markets, such as the fat-tail probability distribution of price returns, the long-range auto-correlation of volatilities, and the persistence probability of volatilities, while it exhibits very different higher-order time correlations of price returns and volatilities, spatial correlations of individual stock prices, and large-fluctuation dynamic behaviors. Furthermore, multi-agent-based models are developed to simulate the microscopic interaction and dynamic evolution of the stock markets.
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Level spacing statistics for two-dimensional massless Dirac billiards
Huang Liang (黄亮), Xu Hong-Ya (徐洪亚), Lai Ying-Cheng (来颖诚), Celso Grebogi
Chin. Phys. B, 2014, 23 (
7
): 070507. DOI:
10.1088/1674-1056/23/7/070507
Abstract
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604
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851
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Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation (orWeyl equation) and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.
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Equivalent formulations of “the equation of life”
Ao Ping (敖平)
Chin. Phys. B, 2014, 23 (
7
): 070513. DOI:
10.1088/1674-1056/23/7/070513
Abstract
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2026
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Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named “the equation of life”. Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerful Boltzmann-Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology.
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Attractive target wave patterns in complex networks consisting of excitable nodes
Zhang Li-Sheng (张立升), Liao Xu-Hong (廖旭红), Mi Yuan-Yuan (弭元元), Qian Yu (钱郁), Hu Gang (胡岗)
Chin. Phys. B, 2014, 23 (
7
): 078906. DOI:
10.1088/1674-1056/23/7/078906
Abstract
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652
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809
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This review describes the investigations of oscillatory complex networks consisting of excitable nodes, focusing on the target wave patterns or say the target wave attractors. A method of dominant phase advanced driving (DPAD) is introduced to reveal the dynamic structures in the networks supporting oscillations, such as the oscillation sources and the main excitation propagation paths from the sources to the whole networks. The target center nodes and their drivers are regarded as the key nodes which can completely determine the corresponding target wave patterns. Therefore, the center (say node
A
) and its driver (say node
B
) of a target wave can be used as a label, (
A,B
), of the given target pattern. The label can give a clue to conveniently retrieve, suppress, and control the target waves. Statistical investigations, both theoretically from the label analysis and numerically from direct simulations of network dynamics, show that there exist huge numbers of target wave attractors in excitable complex networks if the system size is large, and all these attractors can be labeled and easily controlled based on the information given by the labels. The possible applications of the physical ideas and the mathematical methods about multiplicity and labelability of attractors to memory problems of neural networks are briefly discussed.
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Nonequilibrium work equalities in isolated quantum systems
Liu Fei (柳飞), Ouyang Zhong-Can (欧阳钟灿)
Chin. Phys. B, 2014, 23 (
7
): 070512. DOI:
10.1088/1674-1056/23/7/070512
Abstract
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647
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646
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We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, including their origin, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, and recent experimental verifications. Some results are given here for the first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which are useful for understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.
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Sub-diffusive scaling with power-law trapping times
Luo Liang (罗亮), Tang Lei-Han (汤雷翰)
Chin. Phys. B, 2014, 23 (
7
): 070514. DOI:
10.1088/1674-1056/23/7/070514
Abstract
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673
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691
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Thermally driven diffusive motion of a particle underlies many physical and biological processes. In the presence of traps and obstacles, the spread of the particle is substantially impeded, leading to subdiffusive scaling at long times. The statistical mechanical treatment of diffusion in a disordered environment is often quite involved. In this short review, we present a simple and unified view of the many quantitative results on anomalous diffusion in the literature, including the scaling of the diffusion front and the mean first-passage time. Various analytic calculations and physical arguments are examined to highlight the role of dimensionality, energy landscape, and rare events in affecting the particle trajectory statistics. The general understanding that emerges will aid the interpretation of relevant experimental and simulation results.
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Zero-determinant strategy:An underway revolution in game theory
Hao Dong (郝东), Rong Zhi-Hai (荣智海), Zhou Tao (周涛)
Chin. Phys. B, 2014, 23 (
7
): 078905. DOI:
10.1088/1674-1056/23/7/078905
Abstract
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841
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1901
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Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions according to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant (ZD) strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two players, indicating that a smart player can control her unwitting co-player's payoff in a unilateral way [
Proc. Acad. Natl. Sci. USA
109
, 10409 (2012)]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players, and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis, cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.
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Proteins:From sequence to structure
Zheng Wei-Mou (郑伟谋)
Chin. Phys. B, 2014, 23 (
7
): 078705. DOI:
10.1088/1674-1056/23/7/078705
Abstract
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627
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486
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Protein sequences as special heterogeneous sequences are rare in the amino acid sequence space. The specific sequential order of amino acids of a protein is essential to its 3D structure. On the whole, the correlation between sequence and structure of a protein is not so strong. How well would a protein sequence contain its structural information? How does a sequence determine its native structure? Keeping the globular proteins in mind, we discuss several problems from sequence to structure.
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Effective temperature and fluctuation-dissipation theorem in athermal granular systems:A review
Chen Qiong (陈琼), Hou Mei-Ying (厚美瑛)
Chin. Phys. B, 2014, 23 (
7
): 074501. DOI:
10.1088/1674-1056/23/7/074501
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574
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702
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The definition and the previous measurements of a dynamics-relevant temperature-like quantity in granular media are reviewed for slow and fast particle systems. Especially, the validity of the fluctuation-dissipation theorem in such an athermal system is explored. Experimental evidences for the fluctuation-dissipation theorem relevant effect temperature support the athermal statistical mechanics, which has been widely explored in recent years by physicists. Difficulties encountered in defining temperature or establishing thermodynamics or statistical mechanics in non-equilibrium situations are discussed.