統計物理和復雜系統專題編者按

從20世紀中葉至今,復雜系統研究迅速發展,成為了引人注目并具有廣泛應用的新領域.復雜系統要么具有結構的復雜性,要么具有演化的復雜性,在多數情況下二者兼具.不同于傳統物理學通常處理的規則介質,許多復雜系統具有復雜結構,近年來受到極大關注的復雜網絡結構就是其中最典型的代表.同時復雜系統也可表現為演化行為的多樣性和復雜性.即便系統結構并不復雜,系統中的非線性相互作用可能產生復雜的演化行為,包括: 形形色色的不穩定性;豐富的斑圖動力學;各種各樣的自組織、涌現及進化行為等等.物理學從一開始就深深進入了復雜系統研究領域,其中統計物理無疑是研究和理解復雜系統最主要的工具.

復雜系統研究緊密聯系著當前科學發展的兩大趨勢.一是不同學科的交叉和融合.近年來物理學和數學越來越深入地進入其他學科領域,特別是生物學和社會科學,使這些傳統大多以定性描述為主的學科開始了以數據為依托的定量研究,而這些交叉領域研究幾乎都處于復雜系統的研究范疇.二是大數據科學的迅猛發展和應用.基于互聯網和物聯網數據采集和存儲技術的突飛猛進,現在可利用的數據量正在爆炸性的增長.這些數據中包含了極大量對自然和社會的有用信息,能合理利用會帶來巨大并不斷增長的財富.但產生這些數據的系統和可能被這些數據所影響的系統,往往都是復雜系統,其行為具有高度的不可預測性,使這筆財富并不容易獲取.深入研究復雜系統,發展有效的數據分析手段是成功使用這筆潛在財富的關鍵和核心.

要研究和處理所有以上困難和問題,統計物理是強有力的手段.長期以來統計物理在處理各種不可確切預見的軌道和狀態中發展了豐富的思想、方法和技術手段,這些必然將會和已經為復雜系統的研究提供了強有力的工具.同時復雜系統由于結構和行為的大量新特點又為統計物理的創新發展提供強大推動.

本專題邀請了在領域前沿活躍工作的專家學者撰寫了18篇研究和綜述論文,介紹了作者們在該領域的最新進展和成果.內容包括對物理領域以及生物、經濟、工業和其他交叉領域的復雜系統的研究;既有宏觀經典系統的討論,也有量子系統復雜行為的探索;有論文討論了復雜系統行為的基礎統計理論,也有論文分析了復雜系統演化的同步化、斑圖動力學及其調控.專題中多篇論文涉及復雜網絡問題: 有關于網絡結構形成和穩定性分析,也有利用網絡產生的數據分析網絡結構,網絡上信息傳播,網絡結構下人文活動,經濟演化,社會運行規律等等.統計物理和復雜系統是一個內涵宏大的領域,專題論文都是作者興趣所在的課題研究成果和心得,只涉及領域中的點點滴滴.但我們期望專題中介紹的成果能加強國內學者在這一領域的交流,吸引對該領域有興趣的青年學者和學生進來鉆研,推動我國在這一領域的研究水平更上一層.

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