從20世紀(jì)中葉至今,復(fù)雜系統(tǒng)研究迅速發(fā)展,成為了引人注目并具有廣泛應(yīng)用的新領(lǐng)域.復(fù)雜系統(tǒng)要么具有結(jié)構(gòu)的復(fù)雜性,要么具有演化的復(fù)雜性,在多數(shù)情況下二者兼具.不同于傳統(tǒng)物理學(xué)通常處理的規(guī)則介質(zhì),許多復(fù)雜系統(tǒng)具有復(fù)雜結(jié)構(gòu),近年來受到極大關(guān)注的復(fù)雜網(wǎng)絡(luò)結(jié)構(gòu)就是其中最典型的代表.同時(shí)復(fù)雜系統(tǒng)也可表現(xiàn)為演化行為的多樣性和復(fù)雜性.即便系統(tǒng)結(jié)構(gòu)并不復(fù)雜,系統(tǒng)中的非線性相互作用可能產(chǎn)生復(fù)雜的演化行為,包括: 形形色色的不穩(wěn)定性;豐富的斑圖動(dòng)力學(xué);各種各樣的自組織、涌現(xiàn)及進(jìn)化行為等等.物理學(xué)從一開始就深深進(jìn)入了復(fù)雜系統(tǒng)研究領(lǐng)域,其中統(tǒng)計(jì)物理無疑是研究和理解復(fù)雜系統(tǒng)最主要的工具.

復(fù)雜系統(tǒng)研究緊密聯(lián)系著當(dāng)前科學(xué)發(fā)展的兩大趨勢.一是不同學(xué)科的交叉和融合.近年來物理學(xué)和數(shù)學(xué)越來越深入地進(jìn)入其他學(xué)科領(lǐng)域,特別是生物學(xué)和社會(huì)科學(xué),使這些傳統(tǒng)大多以定性描述為主的學(xué)科開始了以數(shù)據(jù)為依托的定量研究,而這些交叉領(lǐng)域研究幾乎都處于復(fù)雜系統(tǒng)的研究范疇.二是大數(shù)據(jù)科學(xué)的迅猛發(fā)展和應(yīng)用.基于互聯(lián)網(wǎng)和物聯(lián)網(wǎng)數(shù)據(jù)采集和存儲(chǔ)技術(shù)的突飛猛進(jìn),現(xiàn)在可利用的數(shù)據(jù)量正在爆炸性的增長.這些數(shù)據(jù)中包含了極大量對(duì)自然和社會(huì)的有用信息,能合理利用會(huì)帶來巨大并不斷增長的財(cái)富.但產(chǎn)生這些數(shù)據(jù)的系統(tǒng)和可能被這些數(shù)據(jù)所影響的系統(tǒng),往往都是復(fù)雜系統(tǒng),其行為具有高度的不可預(yù)測性,使這筆財(cái)富并不容易獲取.深入研究復(fù)雜系統(tǒng),發(fā)展有效的數(shù)據(jù)分析手段是成功使用這筆潛在財(cái)富的關(guān)鍵和核心.

要研究和處理所有以上困難和問題,統(tǒng)計(jì)物理是強(qiáng)有力的手段.長期以來統(tǒng)計(jì)物理在處理各種不可確切預(yù)見的軌道和狀態(tài)中發(fā)展了豐富的思想、方法和技術(shù)手段,這些必然將會(huì)和已經(jīng)為復(fù)雜系統(tǒng)的研究提供了強(qiáng)有力的工具.同時(shí)復(fù)雜系統(tǒng)由于結(jié)構(gòu)和行為的大量新特點(diǎn)又為統(tǒng)計(jì)物理的創(chuàng)新發(fā)展提供強(qiáng)大推動(dòng).

本專題邀請(qǐng)了在領(lǐng)域前沿活躍工作的專家學(xué)者撰寫了18篇研究和綜述論文,介紹了作者們?cè)谠擃I(lǐng)域的最新進(jìn)展和成果.內(nèi)容包括對(duì)物理領(lǐng)域以及生物、經(jīng)濟(jì)、工業(yè)和其他交叉領(lǐng)域的復(fù)雜系統(tǒng)的研究;既有宏觀經(jīng)典系統(tǒng)的討論,也有量子系統(tǒng)復(fù)雜行為的探索;有論文討論了復(fù)雜系統(tǒng)行為的基礎(chǔ)統(tǒng)計(jì)理論,也有論文分析了復(fù)雜系統(tǒng)演化的同步化、斑圖動(dòng)力學(xué)及其調(diào)控.專題中多篇論文涉及復(fù)雜網(wǎng)絡(luò)問題: 有關(guān)于網(wǎng)絡(luò)結(jié)構(gòu)形成和穩(wěn)定性分析,也有利用網(wǎng)絡(luò)產(chǎn)生的數(shù)據(jù)分析網(wǎng)絡(luò)結(jié)構(gòu),網(wǎng)絡(luò)上信息傳播,網(wǎng)絡(luò)結(jié)構(gòu)下人文活動(dòng),經(jīng)濟(jì)演化,社會(huì)運(yùn)行規(guī)律等等.統(tǒng)計(jì)物理和復(fù)雜系統(tǒng)是一個(gè)內(nèi)涵宏大的領(lǐng)域,專題論文都是作者興趣所在的課題研究成果和心得,只涉及領(lǐng)域中的點(diǎn)點(diǎn)滴滴.但我們期望專題中介紹的成果能加強(qiáng)國內(nèi)學(xué)者在這一領(lǐng)域的交流,吸引對(duì)該領(lǐng)域有興趣的青年學(xué)者和學(xué)生進(jìn)來鉆研,推動(dòng)我國在這一領(lǐng)域的研究水平更上一層.

(客座編輯: 北京師范大學(xué) 胡崗;電子科技大學(xué) 周濤;中國科學(xué)院物理研究所 葉方富)

Since the middle of the twentieth century the study of complex systems has been developing rapidly,and now has become a new scientific field of broad applications.Complex systems are defined as systems that have complex structures,complicated dynamics,or,as in most cases,both.Unlike typical physical systems where regular media are considered,complex systems often have complex structures(or media),of which complex networks,attracting great attention in recent decades in both natural and social sciences,are representative examples.On the other hand,regardless of whether the structure is complex or regular,systems can present various complicated behaviors due to their dynamical nonlinearities,such as: various instabilities;rich pattern formation and dynamics;diverse emergent and evolutionary behaviors,and so on.Physics has been involved deeply in the development of this novel field from the beginning.In particular,statistical physics is the main tool for studying and understanding the structural and evolutional rules of complex systems.

The study of complex systems is closely related to two important frontiers.The first is the development of interdisciplinary research.In recent years,physics and mathematics-based tools and thinking have been used more and more extensively in many other fields,such as the biological and social sciences,bringing quantitative computational analyses into these areas which traditionally relied on qualitative descriptions.In this aspect,the analyses of complex systems,in particular complex networks,often serve as an important and in some cases even an irreplaceable foundation.The second frontier is the rapid growth of big data science in recent decades.Due to the fast development of measurement,recording,and storage techniques,data are collected and accumulated at an explosive pace.These data contain an enormous amount of information from both natural and social systems.Extracting and making use of this information are of great interest.However,this is a challenging task,because discernible patterns are typically deeply buried or masked in data produced by complex systems.To realize the full potential of big data,the development of theoretical frameworks and techniques for data analyses of complex systems is critical.

Statistical physics is a powerful approach to tackle the challenges described above.In the past few centuries the field of statistical physics has developed profound and far-reaching ideas,methods,and techniques,for analyzing complicated problems with nondeterministic characteristics.This can offer and has offered powerful tools for studying problems of complex systems.Conversely,novel phenomena,features,and behaviors in complex systems,due to their structural and dynamical complexities,can stimulate conceptual development of statistical physics itself,and help it to explore its capacity further.

For the special issue “statistical physics and complex systems”,a number of leading scientists and experts working actively in this field were invited to contribute research and review papers,and to present their recent research achievements.This body of work investigates complex systems in a wide range of disciplines,including the fields of physics,biology,economical activities,and other natural and social systems.The collection includes discussions on classical systems as well as quantum complex behaviors;descriptions of basic theories of statistical physics of complex systems as well as rich behaviors of pattern formation,pattern dynamics and their controls.Many contributions in this issue address complex network problems,including problems of formation,stability,and reconstruction of network structures,and also dynamical problems of information transport and social activities in networks.Most of the above investigations are based on analyses of available data,both structural data and dynamical data.As the field of statistical physics and complex systems is vast,only a small number of selected areas and topics can be covered in one issue.Nevertheless,we hope that this special issue will enhance academic exchanges among scientists in the field,attract young scientists and students interested in this field to join the research community,and effectively promote research of this exciting emerging field in our country.

Guest editor: Hu Gang(Beijing Normal University,China);Zhou Tao(University of Electronic Science and Technology of China);Ye Fang-Fu(Institute of Physics,Chinese Academy of Sciences)