# 经济物理学

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**Econophysics** is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Some of its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. Econophysics is closely related to social physics.

Econophysics is a heterodox interdisciplinary research field, applying theories and methods originally developed by physicists in order to solve problems in economics, usually those including uncertainty or stochastic processes and nonlinear dynamics. Some of its application to the study of financial markets has also been termed statistical finance referring to its roots in statistical physics. Econophysics is closely related to social physics.

**经济物理学**是一个**非正统的 Heterodox**的跨学科研究领域，通过应用**物理学家 Physicist**开发的理论和方法来解决**经济 Economics**问题，通常包括不确定性或**随机过程 Stochastic Process**和**非线性动力学 Nonlinear Dynamics**。因为它源于**统计物理学 Statistical Physics**，它在金融市场研究中的一些应用也被称为**统计金融学 Statistical Finance**。经济物理学与**社会物理学 Social Physics**密切相关。

## History

历史

Physicists' interest in the social sciences is not new; Daniel Bernoulli, as an example, was the originator of utility-based preferences. One of the founders of neoclassical economic theory, former Yale University Professor of Economics Irving Fisher, was originally trained under the renowned Yale physicist, Josiah Willard Gibbs.^{[1]} Likewise, Jan Tinbergen, who won the first Nobel Memorial Prize in Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University. In particular, Tinbergen developed the gravity model of international trade that has become the workhorse of international economics.

Physicists' interest in the social sciences is not new; Daniel Bernoulli, as an example, was the originator of utility-based preferences. One of the founders of neoclassical economic theory, former Yale University Professor of Economics Irving Fisher, was originally trained under the renowned Yale physicist, Josiah Willard Gibbs. Likewise, Jan Tinbergen, who won the first Nobel Memorial Prize in Economic Sciences in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with Paul Ehrenfest at Leiden University. In particular, Tinbergen developed the gravity model of international trade that has become the workhorse of international economics.

物理学家对**社会科学 Social Sciences**的兴趣并不是什么新鲜事; 例如，**丹尼尔·伯努利 Daniel Bernoulli**就是基于**效用 Utility**的偏好的鼻祖。**新古典主义经济理论 Neoclassical Economic Theory**的创始人之一，前耶鲁大学经济学教授**欧文·费歇尔 Irving Fisher**，最初受训于著名的耶鲁大学**物理学家 Physicist**，**约西亚·威拉德·吉布斯 Josiah Willard Gibbs**。同样，**扬·廷伯根 Jan Tinbergen**，因为开发和应用了经济过程分析的动态模型而获得了1969年的第一个**诺贝尔经济学奖 Nobel Memorial Prize in Economic Sciences**，在**莱顿大学 Leiden University**和 **保罗·埃伦费斯特 Paul Ehrenfest**一起学习了物理学。特别是，Tinbergen 发展了**国际贸易的引力模型 gravity model of international trade**，这个模型已经成为国际经济学的主力。

Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics. Unsatisfied with the traditional explanations and approaches of economists – which usually prioritized simplified approaches for the sake of soluble theoretical models over agreement with empirical data – they applied tools and methods from physics, first to try to match financial data sets, and then to explain more general economic phenomena.

Econophysics was started in the mid-1990s by several physicists working in the subfield of statistical mechanics. Unsatisfied with the traditional explanations and approaches of economists – which usually prioritized simplified approaches for the sake of soluble theoretical models over agreement with empirical data – they applied tools and methods from physics, first to try to match financial data sets, and then to explain more general economic phenomena.

经济物理学是在20世纪90年代中期由几个在**统计力学 Statistical Mechanics**领域工作的物理学家发起的。他们不满足于经济学家的传统解释和方法——这种方法通常优先考虑简化的方法，以便于理解理论模型，而不是与实证数据取得一致——他们应用物理学的工具和方法，首先试图匹配金融数据集，然后解释更普遍的经济现象。

One driving force behind econophysics arising at this time was the sudden availability of large amounts of financial data, starting in the 1980s. It became apparent that traditional methods of analysis were insufficient – standard economic methods dealt with homogeneous agents and equilibrium, while many of the more interesting phenomena in financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.

One driving force behind econophysics arising at this time was the sudden availability of large amounts of financial data, starting in the 1980s. It became apparent that traditional methods of analysis were insufficient – standard economic methods dealt with homogeneous agents and equilibrium, while many of the more interesting phenomena in financial markets fundamentally depended on heterogeneous agents and far-from-equilibrium situations.

当时经济物理学兴起的一个推动力是，自1980年代开始，突然出现了大量的金融数据。显而易见，传统的分析方法是不够充分的——标准的经济学方法处理同质的主体和，而金融市场中许多更有趣的现象从根本上依赖于**异质的 Heterogeneous**主体和远离均衡的情况。

The term "econophysics" was coined by H. Eugene Stanley, to describe the large number of papers written by physicists in the problems of (stock and other) markets, in a conference on statistical physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996.^{[2]}^{[3]} The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.^{[4]}

The term "econophysics" was coined by H. Eugene Stanley, to describe the large number of papers written by physicists in the problems of (stock and other) markets, in a conference on statistical physics in Kolkata (erstwhile Calcutta) in 1995 and first appeared in its proceedings publication in Physica A 1996. The inaugural meeting on econophysics was organised in 1998 in Budapest by János Kertész and Imre Kondor. The first book on econophysics was by R. N. Mantegna & H. E. Stanley in 2000.

“经济物理学”一词是由**H·尤金·斯坦利 H·Eugene Stanley** 于1995年在**加尔各答 Kolkata**(昔日的**加尔各答 Calcutta**)的一次统计物理学会议上发明的，用来描述物理学家们在(股票和其他)市场问题上撰写的大量论文，这些论文首次出现在1996年在**《Physica A》** 出版的会议记录中。经济物理学会议于1998年在布达佩斯由**János Kertész** 和**Imre Kondor**举办。2000年，r. n. Mantegna & h. e. Stanley 出版了第一本关于经济物理学的书。

The almost regular meeting series on the topic include: ECONOPHYS-KOLKATA (held in Kolkata & Delhi),^{[5]} Econophysics Colloquium, ESHIA/ WEHIA.

The almost regular meeting series on the topic include: ECONOPHYS-KOLKATA (held in Kolkata & Delhi), Econophysics Colloquium, ESHIA/ WEHIA.

关于这一主题的几乎定期的会议系列包括: 经济学-加尔各答 (在加尔各答和德里举行)、 经济物理学座谈会、 ESHIA/WEHIA。

In recent years network science, heavily reliant on analogies from statistical mechanics, has been applied to the study of productive systems. That is the case with the works done at the Santa Fe Institute in European Funded Research Projects as Forecasting Financial Crises and the Harvard-MIT Observatory of Economic Complexity

In recent years network science, heavily reliant on analogies from statistical mechanics, has been applied to the study of productive systems. That is the case with the works done at the Santa Fe Institute in European Funded Research Projects as Forecasting Financial Crises and the Harvard-MIT Observatory of Economic Complexity

近年来，**网络科学 Network Science**，严重依赖于**统计力学 Statistical Mechanics**的类推，已经应用于生产系统的研究。**圣菲研究所 Santa Fe Institute**在欧洲资助的研究预测金融危机的项目和哈佛-麻省理工学院经济复杂性观测站的工作就是如此。

If "econophysics" is taken to denote the principle of applying statistical mechanics to economic analysis, as opposed to a particular literature or network, priority of innovation is probably due to Emmanuel Farjoun and Moshé Machover (1983). Their book *Laws of Chaos: A Probabilistic Approach to Political Economy* proposes *dis*solving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.^{[6]}

If "econophysics" is taken to denote the principle of applying statistical mechanics to economic analysis, as opposed to a particular literature or network, priority of innovation is probably due to Emmanuel Farjoun and Moshé Machover (1983). Their book Laws of Chaos: A Probabilistic Approach to Political Economy proposes dissolving (their words) the transformation problem in Marx's political economy by re-conceptualising the relevant quantities as random variables.

如果说“经济物理学”指的是将统计力学应用于经济分析的原则，而不是某一特定的文献或网络，那么创新的优先权可能应归功于 Emmanuel Farjoun 和**Moshé Machover**(1983)。他们在《混沌定律: 政治经济学的概率方法》一书中提出，通过将相关数量重新概念化为随机变量，来解决(他们的话)马克思政治经济学中的**转换问题 Transformation Problem**。

If, on the other hand, "econophysics" is taken to denote the application of physics to economics, one can consider the works of Léon Walras and Vilfredo Pareto as part of it. Indeed, as shown by Bruna Ingrao and Giorgio Israel, general equilibrium theory in economics is based on the physical concept of mechanical equilibrium.

If, on the other hand, "econophysics" is taken to denote the application of physics to economics, one can consider the works of Léon Walras and Vilfredo Pareto as part of it. Indeed, as shown by Bruna Ingrao and Giorgio Israel, general equilibrium theory in economics is based on the physical concept of mechanical equilibrium.

另一方面，如果把“经济物理学”看作是物理学在经济学中的应用，那么可以把**列昂·瓦尔拉斯 Léon Walras**和**维尔弗雷多·帕雷托 Vilfredo Pareto**的著作看作是其中的一部分。事实上，正如**布鲁娜·因格罗 Bruna Ingrao**和**乔治·以色列 Giorgio Israel**所表明的那样，经济学中的**一般均衡理论 general equilibrium theory**是基于**力学平衡 mechanical equilibrium**的物理概念。

Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with neo-Ricardianism. Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, J. Doyne Farmer, Diego Garlaschelli, Dirk Helbing, János Kertész, Francis Longstaff, Rosario N. Mantegna, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang. Particularly noteworthy among the formal courses on econophysics is the one offered by Diego Garlaschelli at the Physics Department of the Leiden University,^{[7]}^{[8]} from where the first Nobel-laureate in economics Jan Tinbergen came. From September 2014 King's College has awarded the first position of Full Professor in Econophysics.

Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with neo-Ricardianism. Notable econophysicists are Jean-Philippe Bouchaud, Bikas K Chakrabarti, J. Doyne Farmer, Diego Garlaschelli, Dirk Helbing, János Kertész, Francis Longstaff, Rosario N. Mantegna, Matteo Marsili, Joseph L. McCauley, Enrico Scalas, Didier Sornette, H. Eugene Stanley, Victor Yakovenko and Yi-Cheng Zhang. Particularly noteworthy among the formal courses on econophysics is the one offered by Diego Garlaschelli at the Physics Department of the Leiden University, from where the first Nobel-laureate in economics Jan Tinbergen came. From September 2014 King's College has awarded the first position of Full Professor in Econophysics.

经济物理学同 **伊恩·斯蒂德曼 Ian Steedman**和其他**新李嘉图学派 neo-Ricardianism**相关的人提出的经济学的物理量方法没有任何关系。值得注意的经济物理学家有，**让-菲利普·布查德 Jean-Philippe Bouchaud**,**比卡斯·K·查克拉巴蒂 Bikas K Chakrabarti**,**J·杜恩·法默 J.Doyne Farmer**,**迭戈·加拉斯切利 Diego Garlaschelli**,**德克·赫尔宾 Dirk Helbing**,**János Kertész**,**弗朗西斯·朗斯塔夫 Francis Longstaff**,**罗萨里奥·N·曼特尼亚 Rosario N. Mantegna**,**马泰奥·马希里 Matteo Marsili**,**约瑟夫·L·麦考利 Joseph L. McCauley**,**恩里科·斯卡拉斯 Enrico Scalas**,**迪迪埃·索内特 Didier Sornette**,**H·尤金·斯坦利 H. Eugene Stanley**,**维克托·雅科文科 Victor Yakovenko**和张翼成 .在经济物理学的正规课程中，特别值得一提的是莱顿大学物理系的 Diego Garlaschelli 开设的一门课程，他就是第一位诺贝尔经济学奖得主 Jan Tinbergen 的后生。由2014年9月起，英皇书院授予经济物理学首个全职教授职位。

## Basic tools

基本工具

Basic tools of econophysics are probabilistic and statistical methods often taken from statistical physics.

Basic tools of econophysics are probabilistic and statistical methods often taken from statistical physics.

经济物理学的基本工具是通常取自统计物理学的**概率 Probability**和**统计 Statistics**方法。

Physics models that have been applied in economics include the kinetic theory of gas (called the kinetic exchange models of markets ^{[9]}), percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction.^{[10]} Moreover, there have been attempts to use the mathematical theory of complexity and information theory, as developed by many scientists among whom are Murray Gell-Mann and Claude E. Shannon, respectively.

Physics models that have been applied in economics include the kinetic theory of gas (called the kinetic exchange models of markets ), percolation models, chaotic models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for earthquake prediction. Moreover, there have been attempts to use the mathematical theory of complexity and information theory, as developed by many scientists among whom are Murray Gell-Mann and Claude E. Shannon, respectively.

应用于经济学的物理模型包括**气体动力学理论 kinetic theory of gas**(称为**市场动力学交换模型 kinetic exchange models of markets**)、**逾渗 percolation**模型、用于研究心脏骤停的**混沌 chaotic**模型、具有**自组织临界性 self-organizing criticality**的模型以及其他用于**地震预测 earthquake prediction**的模型。此外，还有人试图使用**复杂性 complexity**数学理论和**信息论 information theory**，这两种理论是由许多科学家发展起来的，其中分别有**默里·盖尔曼 Murray Gell-Mann**和**克劳德·E·香农 Claude E. Shannon**。

For potential games, it has been shown that an emergence-producing equilibrium based on information via Shannon information entropy produces the same equilibrium measure (Gibbs measure from statistical mechanics) as a stochastic dynamical equation, both of which are based on bounded rationality models used by economists.^{[11]}

For potential games, it has been shown that an emergence-producing equilibrium based on information via Shannon information entropy produces the same equilibrium measure (Gibbs measure from statistical mechanics) as a stochastic dynamical equation, both of which are based on bounded rationality models used by economists.

对于**势博弈 Potential game**，已经证明了一个基于信息的涌现均衡通过香农熵产生了与随机动力方程相同的均衡测度(来自统计力学的**吉布斯测度 Gibbs measure**) ，这两者都是基于经济学家使用的**有限理性 Bounded Rationality**模型。

The fluctuation-dissipation theorem connects the two to establish a concrete correspondence of "temperature", "entropy", "free potential/energy", and other physics notions to an economics system. The statistical mechanics model is not constructed a-priori - it is a result of a boundedly rational assumption and modeling on existing neoclassical models. It has been used to prove the "inevitability of collusion" result of Huw Dixon in a case for which the neoclassical version of the model does not predict collusion.^{[12]}

The fluctuation-dissipation theorem connects the two to establish a concrete correspondence of "temperature", "entropy", "free potential/energy", and other physics notions to an economics system. The statistical mechanics model is not constructed a-priori - it is a result of a boundedly rational assumption and modeling on existing neoclassical models. It has been used to prove the "inevitability of collusion" result of Huw Dixon in a case for which the neoclassical version of the model does not predict collusion.

涨落耗散定理将二者联系起来，建立了“温度”、“熵”、“自由势/能”以及其他物理概念与经济系统的具体对应关系。统计力学模型不是先验构建的，它是有限理性假设和现有新古典主义模型建模的结果。在一个新古典主义模型不能预测合谋的案例中，它被用来证明**休·迪克森 Huw Dixon**的“合谋的必然性”结果。

Here the demand is increasing, as with Veblen goods or stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful.^{[13]}

Here the demand is increasing, as with Veblen goods or stock buyers with the "hot hand" fallacy preferring to buy more successful stocks and sell those that are less successful.

这里的需求正在增加，就像**韦伯伦商品 Veblen good** 或有**短期持续性 Hot Hand**谬论的股票买家，他们更愿意买入更多成功的股票，卖出那些不那么成功的股票。

Vernon L. Smith used these techniques to model sociability in economics.^{[14]} There, a model correctly predicts that agents are averse to resentment and punishment, and that there is an asymmetry between gratitude/reward and resentment/punishment. The classical Nash equilibrium is shown to have *no* predictive power for that model, and the Gibbs equilibrium must be used to predict phenomena outlined in *Humanomics*.^{[15]}

Vernon L. Smith used these techniques to model sociability in economics. There, a model correctly predicts that agents are averse to resentment and punishment, and that there is an asymmetry between gratitude/reward and resentment/punishment. The classical Nash equilibrium is shown to have no predictive power for that model, and the Gibbs equilibrium must be used to predict phenomena outlined in Humanomics.

**弗农·L·史密斯 Vernon L. Smith**利用这些技巧为经济学中的社交性建立了模型。在这里，一个模型正确地预测了行为主体反对怨恨和惩罚，以及感激/奖励和怨恨/惩罚之间的不对称情况。经典的纳什均衡点模型对这个模型没有预测能力，吉布斯平衡必须在 Humanomics 概述的现象中进行预测。

Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets.^{[16]}

Quantifiers derived from information theory were used in several papers by econophysicist Aurelio F. Bariviera and coauthors in order to assess the degree in the informational efficiency of stock markets.

经济物理学家**奥雷里奥·F·巴里维拉 Aurelio F. Bariviera**和合著者在几篇论文中使用了来自**信息论 information theory**的量词，以评估股票市场信息效率的程度。

Zunino et al. use an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This Cartesian representation establish an efficiency ranking of different markets and distinguish different bond market dynamics. Moreover, the authors conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. A similar study developed by Bariviera et al.^{[17]} explore the relationship between credit ratings and informational efficiency of a sample of corporate bonds of US oil and energy companies using also the complexity–entropy causality plane. They find that this classification agrees with the credit ratings assigned by Moody's.

Zunino et al. use an innovative statistical tool in the financial literature: the complexity-entropy causality plane. This Cartesian representation establish an efficiency ranking of different markets and distinguish different bond market dynamics. Moreover, the authors conclude that the classification derived from the complexity-entropy causality plane is consistent with the qualifications assigned by major rating companies to the sovereign instruments. A similar study developed by Bariviera et al. explore the relationship between credit ratings and informational efficiency of a sample of corporate bonds of US oil and energy companies using also the complexity–entropy causality plane. They find that this classification agrees with the credit ratings assigned by Moody's.

祖尼诺等人，在金融文献中使用创新的统计工具: 复杂性-熵因果关系平面。这种笛卡尔式表示建立了不同市场的效率排名，并区分了不同的债券市场动态。此外，从复杂熵因果关系平面导出的分类结果与主权证券评级公司对主权证券的评级结果一致。同时由 Bariviera 等人开发的一个类似的研究，以美国石油和能源公司债券为样本，运用复杂熵因果关系平面，探讨了信用评级与信息效率的关系。他们发现，这一分类与穆迪给予的信用评级相一致。

Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices. One paper has argued that this technique can improve the performance of portfolios, e.g., in applied in portfolio optimization.^{[18]}

Another good example is random matrix theory, which can be used to identify the noise in financial correlation matrices. One paper has argued that this technique can improve the performance of portfolios, e.g., in applied in portfolio optimization.

另一个很好的例子是**随机矩阵理论 random matrix theory**，它可以用来识别金融相关矩阵中的噪声。一篇论文认为，这种技术可以改善投资组合的性能，例如，应用于**portfolio optimization 投资组合优化**。

There are, however, various other tools from physics that have so far been used, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economics and quantum finance),^{[19]} and the path integral formulation of statistical mechanics.^{[20]}

There are, however, various other tools from physics that have so far been used, such as fluid dynamics, classical mechanics and quantum mechanics (including so-called classical economy, quantum economics and quantum finance), and the path integral formulation of statistical mechanics.

然而，到目前为止，还有其他各种各样的物理学工具被使用，例如**流体动力学 fluid dynamics**、**经典力学 classical mechanics**和**量子力学 quantum mechanics**(包括所谓的**古典经济学 classical economy**、**量子经济学 quantum economics**和**量子金融学 quantum finance**) ，以及**路径积分表述 path integral formulation**统计力学。

The concept of economic complexity index, introduced by the MIT physicist Cesar A. Hidalgo and the Harvard economist Ricardo Hausmann and made available at MIT's Observatory of Economic Complexity, has been devised as a predictive tool for economic growth. According to the estimates of Hausmann and Hidalgo, the ECI is far more accurate in predicting GDP growth than the traditional governance measures of the World Bank.^{[21]}

The concept of economic complexity index, introduced by the MIT physicist Cesar A. Hidalgo and the Harvard economist Ricardo Hausmann and made available at MIT's Observatory of Economic Complexity, has been devised as a predictive tool for economic growth. According to the estimates of Hausmann and Hidalgo, the ECI is far more accurate in predicting GDP growth than the traditional governance measures of the World Bank.

**经济复杂性指数 economic complexity index**的概念，由麻省理工学院的物理学家**塞萨尔·A·希达尔戈 Cesar a. Hidalgo**和哈佛大学的经济学家**里卡多·豪斯曼 Ricardo Hausmann ** 提出，并在麻省理工学院的**经济复杂性观察站 Observatory of Economic Complexity**提供，已经被设计成**经济增长的预测工具 predictive tool for economic growth**。根据 Hausmann 和 Hidalgo 的估计，与**世界银行 World Bank**的传统治理措施相比，出口信贷保险在预测 GDP 增长方面要准确得多。

There are also analogies between finance theory and diffusion theory. For instance, the Black–Scholes equation for option pricing is a diffusion-advection equation (see however ^{[22]}^{[23]} for a critique of the Black–Scholes methodology). The Black–Scholes theory can be extended to provide an analytical theory of main factors in economic activities.^{[20]}

There are also analogies between finance theory and diffusion theory. For instance, the Black–Scholes equation for option pricing is a diffusion-advection equation (see however for a critique of the Black–Scholes methodology). The Black–Scholes theory can be extended to provide an analytical theory of main factors in economic activities. Other economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics. More recently, Vernon L. Smith, one of the founders of experimental economics and Nobel Memorial Prize in Economic Sciences laureate, has used these techniques and claimed they show a lot of promise. Also several scaling laws have been found in various economic data.

在金融理论和**扩散 Diffusion**理论之间也有相似之处。例如，期权定价的**布莱克-斯科尔斯方程 Black–Scholes equation**是一个**扩散-对流 diffusion-advection**方程(见对布莱克-斯科尔斯方法论的批判)。布莱克-斯科尔斯理论可以扩展为经济活动中主要因素的分析理论。其他经济学家，包括毛罗 · 加勒盖蒂，史蒂夫 · 基恩，保罗 · 奥默罗德和艾伦 · 基尔曼对此表现出了更多的兴趣，但也批评了经济物理学的一些趋势。最近，实验经济学创始人之一、诺贝尔经济学奖得主弗农·L·史密斯使用了这些技术，并声称它们表现出良好的前景。在各种经济数据中也发现了一些标度律。

Presently, one of the main results of econophysics comprises the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data), arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the risks, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a failure probability of only [math]\displaystyle{ P\propto x^{-4}\,, }[/math] where x is an increasingly large variable in the tail region of the distribution considered (i.e. a price statistics with much more than 10^{8} data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away". The "fat tails" are also observed in commodity markets.

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的“肥尾”解释为一种普遍的自相似标度性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了风险，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有[math]\displaystyle{ P\propto x^{-4}\,, }[/math]其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过10^{8})。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。商品市场也出现了“肥尾”现象。

## Influence

影响

As in quantum field theory the "fat tails" can be obtained by complicated "nonperturbative" methods, mainly by numerical ones, since they contain the deviations from the usual Gaussian approximations, e.g. the Black–Scholes theory. Fat tails can, however, also be due to other phenomena, such as a random number of terms in the central-limit theorem, or any number of other, non-econophysics models. Due to the difficulty in testing such models, they have received less attention in traditional economic analysis.

正如在量子场论中一样，“肥尾”可以通过复杂的“非微扰”方法得到，主要是通过数值方法，因为它们包含了通常的高斯近似的偏差，例如:布莱克-斯科尔斯理论。然而，肥尾也可能是由其他现象引起的，比如中心极限定理中的随机项数，或者其他任何非经济物理学模型。由于这些模型难以检验，因此在传统的经济分析中很少受到重视。

Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals. Some Mainstream economists have generally been unimpressed by this work.^{[24]} Other economists, including Mauro Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more interest, but also criticized some trends in econophysics. More recently, Vernon L. Smith, one of the founders of experimental economics and Nobel Memorial Prize in Economic Sciences laureate, has used these techniques and claimed they show a lot of promise.^{[14]}

关于经济物理学的论文主要发表在专门研究物理学和统计力学的期刊上，而不是主要的经济学期刊上。一些**主流经济学家 Mainstream economics**普遍对这项研究不以为然。其他经济学家，包括**毛罗·加勒盖蒂 Mauro Gallegati **，**史蒂夫·基恩 Steve Keen**，**保罗·奥默罗德 Paul Ormerod**和艾伦·基尔曼对此表现出了更多的兴趣，但也批评了经济物理学的一些趋势。最近，**实验经济学 experimental economics**创始人之一、**诺贝尔经济学奖 Nobel Memorial Prize in Economic Sciences**得主**弗农·L·史密斯 Vernon L. Smith**使用了这些技术，并声称它们表现出良好的前景。

Econophysics is having some impacts on the more applied field of quantitative finance, whose scope and aims significantly differ from those of economic theory. Various econophysicists have introduced models for price fluctuations in physics of financial markets or original points of view on established models.^{[22]}^{[25]}^{[26]} Also several scaling laws have been found in various economic data.^{[27]}^{[28]}^{[29]}

经济物理学对**定量金融学 quantitative finance**的应用领域产生了一定的影响，定量金融学的研究范围和研究目标与经济学理论有很大的不同。各种经济物理学家介绍了**金融市场物理学 physics of financial markets**中的价格波动模型或已建立模型的原始观点。在各种经济数据中也发现了一些标度律。

## Main results

主要成果

Presently, one of the main results of econophysics comprises the explanation of the "fat tails" in the distribution of many kinds of financial data as a universal self-similar scaling property (i.e. scale invariant over many orders of magnitude in the data),^{[30]} arising from the tendency of individual market competitors, or of aggregates of them, to exploit systematically and optimally the prevailing "microtrends" (e.g., rising or falling prices). These "fat tails" are not only mathematically important, because they comprise the risks, which may be on the one hand, very small such that one may tend to neglect them, but which - on the other hand - are not negligible at all, i.e. they can never be made exponentially tiny, but instead follow a measurable algebraically decreasing power law, for example with a *failure probability* of only [math]\displaystyle{ P\propto x^{-4}\,, }[/math] where *x* is an increasingly large variable in the tail region of the distribution considered (i.e. a price statistics with much more than 10^{8} data). I.e., the events considered are not simply "outliers" but must really be taken into account and cannot be "insured away".^{[31]} It appears that it also plays a role that near a change of the tendency (e.g. from falling to rising prices) there are typical "panic reactions" of the selling or buying agents with algebraically increasing bargain rapidities and volumes.^{[31]} The "fat tails" are also observed in commodity markets.

目前，经济物理学的主要研究成果之一是将多种金融数据分布中的**肥尾 fat tails**解释为一种**通用的 universal**自相似**标度 scaling**性质(即“肥尾”)。由于个别市场竞争对手或他们的整体趋势有系统和最佳地利用当前的「微观趋势」(例如，价格上升或下跌)而引起的数量级。这些“肥尾”不仅在数学上很重要，因为它们包含了**风险 risk**，这些风险一方面可能非常小，以至于人们可能会忽略它们，但另一方面，这些风险一点也不可忽视。它们永远不可能成指数微小，而是遵循一个可测量的代数递减幂律，例如，故障概率只有[math]\displaystyle{ P\propto x^{-4}\,, }[/math]其中x在所考虑的分布的尾部区域是一个越来越大的变量(例如，x = 0。一个价格统计数据远远超过10^{8})。也就是说，所考虑的事件不仅仅是“异常值” ，而是必须真正加以考虑，不能“保走”。**商品市场 commodity market**也出现了“肥尾”现象。

As in quantum field theory the "fat tails" can be obtained by complicated "nonperturbative" methods, mainly by numerical ones, since they contain the deviations from the usual Gaussian approximations, e.g. the Black–Scholes theory. Fat tails can, however, also be due to other phenomena, such as a random number of terms in the central-limit theorem, or any number of other, non-econophysics models. Due to the difficulty in testing such models, they have received less attention in traditional economic analysis.

正如在量子场论中一样，“肥尾”可以通过复杂的**非微扰 nonperturbative**方法得到，主要是通过数值方法，因为它们包含了通常的** 高斯近似Gaussian approximations**的偏差，例如:**布莱克-斯科尔斯 Black–Scholes**理论。然而，肥尾也可能是由其他现象引起的，比如中心极限定理中的随机项数，或者其他任何非经济物理学模型。由于这些模型难以检验，因此在传统的经济分析中很少受到重视。

## See also

- Bose–Einstein condensation (network theory)玻色-爱因斯坦凝聚(网络理论)

- Complexity economics复杂性经济学

- Complex network复杂网络

- Kinetic exchange models of markets市场的动态交换模型

- Network theory网络理论

- Network science网络科学

- Thermoeconomics热经济学

- Quantum finance量子金融学

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- ↑ Yale Economic Review, Retrieved October-25-09 -{zh-cn:互联网档案馆; zh-tw:網際網路檔案館; zh-hk:互聯網檔案館;}-的存檔，存档日期2008-05-08.
- ↑ Interview of H. E. Stanley on Econophysics (Published in "IIM Kozhikode Society & Management Review", Sage publication (USA), Vol. 2 Issue 2 (July), pp. 73-78 (2013))
- ↑ Econophysics Research in India in the last two Decades (1993-2013) (Published in "IIM Kozhikode Society & Management Review", Sage publication (USA), Vol. 2 Issue 2 (July), pp. 135-146 (2013))
- ↑ "An Introduction to Econophysics", Cambridge University Press, Cambridge (2000)
- ↑ "Econophysics of Wealth Distributions", Eds. A. Chatterjee et al., New Economic Windows, Springer, Milan (2005), & the subsequent eight Proc. Volumes published in 2006, 2007, 2010, 2011, 2013, 2014, 2015 & 2019 in the New Economic Windows series of Springer
- ↑ Farjoun and Machover disclaim complete originality: their book is dedicated to the late Robert H. Langston, who they cite for direct inspiration (page 12), and they also note an independent suggestion in a discussion paper by E.T. Jaynes (page 239)
- ↑ "Econophysics, 2012-2013 ~ e-Prospectus, Leiden University".
*studiegids.leidenuniv.nl*(in English). Retrieved 2018-09-10. - ↑ "Econophysics, 2020-2021 ~ e-Prospectus, Leiden University".
*studiegids.leidenuniv.nl*(in English). Retrieved 2020-09-05. - ↑ Bikas K Chakrabarti, Anirban Chakraborti, Satya R Chakravarty, Arnab Chatterjee (2012).
*Econophysics of Income & Wealth Distributions*. Cambridge University Press, Cambridge. - ↑ Didier Sornette (2003).
*Why Stock Markets Crash?*. Princeton University Press. - ↑ Campbell, Michael J. (2005). "A Gibbsian approach to potential game theory". arXiv:cond-mat/0502112v2.
- ↑ Dixon, Huw (2000). "keeping up with the Joneses: competition and the evolution of collusion".
*Journal of Economic Behavior and Organization*.**43**(2): 223–238. doi:10.1016/s0167-2681(00)00117-7. - ↑ Johnson, Joseph; Tellis, G.J.; Macinnis, D.J. (2005). "Losers, Winners, and Biased Trades".
*Journal of Consumer Research*.**2**(32): 324–329. doi:10.1086/432241. Unknown parameter`|s2cid=`

ignored (help) - ↑
^{14.0}^{14.1}Michael J. Campbell; Vernon L. Smith (2020). "An elementary humanomics approach to boundedly rational quadratic models".*Physica A*.**562**: 125309. doi:10.1016/j.physa.2020.125309. - ↑ Vernon L. Smith and Bart J. Wilson (2019).
*Humanomics: Moral Sentiments and the Wealth of Nations for the Twenty-First Century*. Cambridge University Press. doi:10.1017/9781108185561. ISBN 9781108185561. https://www.cambridge.org/core/books/humanomics/1B4064A206BD99DB36E794B53ADF8BB4. - ↑ Zunino, L., Bariviera, A.F., Guercio, M.B., Martinez, L.B. and Rosso, O.A. (2012). "On the efficiency of sovereign bond markets" (PDF).
*Physica A: Statistical Mechanics and Its Applications*.**391**(18): 4342–4349. Bibcode:2012PhyA..391.4342Z. doi:10.1016/j.physa.2012.04.009. hdl:11336/59368. Unknown parameter`|s2cid=`

ignored (help)CS1 maint: multiple names: authors list (link) - ↑ Bariviera, A.F., Zunino, L., Guercio, M.B., Martinez, L.B. and Rosso, O.A. (2013). "Efficiency and credit ratings: a permutation-information-theory analysis" (PDF).
*Journal of Statistical Mechanics: Theory and Experiment*.**2013**(8): P08007. arXiv:1509.01839. Bibcode:2013JSMTE..08..007F. doi:10.1088/1742-5468/2013/08/P08007. hdl:11336/2007. Unknown parameter`|s2cid=`

ignored (help)CS1 maint: multiple names: authors list (link) - ↑ Vasiliki Plerou; Parameswaran Gopikrishnan; Bernd Rosenow; Luis Amaral; Thomas Guhr; H. Eugene Stanley (2002). "Random matrix approach to cross correlations in financial data".
*Physical Review E*.**65**(6): 066126. arXiv:cond-mat/0108023. Bibcode:2002PhRvE..65f6126P. doi:10.1103/PhysRevE.65.066126. PMID 12188802. Unknown parameter`|s2cid=`

ignored (help) - ↑ Anatoly V. Kondratenko (2015).
*Probabilistic Economic Theory*. ISBN 978-5-02-019121-1. - ↑
^{20.0}^{20.1}Chen, Jing (2015).*The Unity of Science and Economics: A New Foundation of Economic Theory*. https://www.springer.com/us/book/9781493934645: Springer. - ↑ Ricardo Hausmann; Cesar Hidalgo; et al. "The Atlas of Economic Complexity". The Observatory of Economic Complexity (MIT Media Lab). Retrieved 26 April 2012.
- ↑
^{22.0}^{22.1}Jean-Philippe Bouchaud; Marc Potters (2003).*Theory of Financial Risk and Derivative Pricing*. Cambridge University Press. https://archive.org/details/theoryoffinancia0000bouc. - ↑ Bouchaud, J-P.; Potters, M. (2001). "Welcome to a non-Black-Scholes world".
*Quantitative Finance*.**1**(5): 482–483. doi:10.1080/713665871. Unknown parameter`|s2cid=`

ignored (help) - ↑ Philip Ball (2006). "Econophysics: Culture Crash".
*Nature*.**441**(7094): 686–688. Bibcode:2006Natur.441..686B. CiteSeerX 10.1.1.188.8120. doi:10.1038/441686a. PMID 16760949. Unknown parameter`|s2cid=`

ignored (help) - ↑ Enrico Scalas (2006). "The application of continuous-time random walks in finance and economics".
*Physica A*.**362**(2): 225–239. Bibcode:2006PhyA..362..225S. doi:10.1016/j.physa.2005.11.024. - ↑ Y. Shapira; Y. Berman; E. Ben-Jacob (2014). "Modelling the short term herding behaviour of stock markets".
*New Journal of Physics*.**16**(5): 053040. Bibcode:2014NJPh...16e3040S. doi:10.1088/1367-2630/16/5/053040. - ↑ Y. Liu; P. Gopikrishnan; P. Cizeau; M. Meyer; C.-K. Peng; H. E. Stanley (1999). "Statistical properties of the volatility of price fluctuations".
*Physical Review E*.**60**(2): 1390–400. arXiv:cond-mat/9903369. Bibcode:1999PhRvE..60.1390L. CiteSeerX 10.1.1.241.9346. doi:10.1103/PhysRevE.60.1390. PMID 11969899. Unknown parameter`|s2cid=`

ignored (help) - ↑ M. H. R. Stanley; L. A. N. Amaral; S. V. Buldyrev; S. Havlin; H. Leschhorn; P. Maass; M. A. Salinger; H. E. Stanley (1996). "Scaling behaviour in the growth of companies".
*Nature*.**379**(6568): 804. Bibcode:1996Natur.379..804S. doi:10.1038/379804a0. Unknown parameter`|s2cid=`

ignored (help) - ↑ K. Yamasaki; L. Muchnik; S. Havlin; A. Bunde; H.E. Stanley (2005). "Scaling and memory in volatility return intervals in financial markets".
*PNAS*.**102**(26): 9424–8. Bibcode:2005PNAS..102.9424Y. doi:10.1073/pnas.0502613102. PMC 1166612. PMID 15980152. - ↑ The physicists noted the scaling behaviour of "fat tails" through a letter to the scientific journal
*Nature*by Rosario N. Mantegna and H. Eugene Stanley:*Scaling behavior in the dynamics of an economic index*, Nature Vol. 376, pages 46-49 (1995) - ↑
^{31.0}^{31.1}See for example Preis, Mantegna, 2003.

## Further reading

- Rosario N. Mantegna, H. Eugene Stanley,
*An Introduction to Econophysics: Correlations and Complexity in Finance*, Cambridge University Press (Cambridge, UK, 1999)

- Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti, Bikas K Chakrabarti.
*Econophysics: An Introduction*, Wiley-VCH (2010)

- Bikas K Chakrabarti, Anirban Chakraborti, Arnab Chatterjee,
*Econophysics and Sociophysics : Trends and Perspectives*, Wiley-VCH, Berlin (2006)

- Joseph McCauley,
*Dynamics of Markets, Econophysics and Finance*, Cambridge University Press (Cambridge, UK, 2004)

- Bertrand Roehner,
*Patterns of Speculation - A Study in Observational Econophysics*, Cambridge University Press (Cambridge, UK, 2002)

- Surya Y., Situngkir, H., Dahlan, R. M., Hariadi, Y., Suroso, R. (2004).
*Aplikasi Fisika dalam Analisis Keuangan (Physics Applications in Financial Analysis*. Bina Sumber Daya MIPA.

- Arnab Chatterjee, Sudhakar Yarlagadda, Bikas K Chakrabarti,
*Econophysics of Wealth Distributions*, Springer-Verlag Italia (Milan, 2005)https://en.wikipedia.org/wiki/Defekte_Weblinks?dwl={{{url}}} Seite nicht mehr abrufbar], Suche in Webarchiven: Kategorie:Wikipedia:Weblink offline (andere Namensräume)[http://timetravel.mementoweb.org/list/2010/Kategorie:Wikipedia:Vorlagenfehler/Vorlage:Toter Link/URL_fehlt

- Philip Mirowski,
*More Heat than Light - Economics as Social Physics, Physics as Nature's Economics*, Cambridge University Press (Cambridge, UK, 1989)

- Ubaldo Garibaldi and Enrico Scalas,
*Finitary Probabilistic Methods in Econophysics*, Cambridge University Press (Cambridge, UK, 2010).

- Emmanual Farjoun and Moshé Machover,
*Laws of Chaos: a probabilistic approach to political economy*, Verso (London, 1983)

- Marcelo Byrro Ribeiro,
*Income Distribution Dynamics of Economic Systems: An Econophysical Approach*, Cambridge University Press (Cambridge, UK, 2020).

- Nature Physics Focus issue: Complex networks in finance March 2013 Volume 9 No 3 pp 119–128

- Mark Buchanan,
*What has econophysics ever done for us?*, Nature 2013

- An Analytical treatment of Gibbs-Pareto behaviour in wealth distribution by Arnab Das and Sudhakar Yarlagadda 模板:ArXiv

- A distribution function analysis of wealth distribution by Arnab Das and Sudhakar Yarlagadda 模板:ArXiv

- Analytical treatment of a trading market model by Arnab Das 模板:ArXiv

- Martin Shubik and Eric Smith,
*The Guidance of an Enterprise Economy*, MIT Press, [1] MIT Press (2016)

- Abergel, F., Aoyama, H., Chakrabarti, B.K., Chakraborti, A., Deo, N., Raina, D., Vodenska, I. (Eds.),
*Econophysics and Sociophysics: Recent Progress and Future Directions*, [2], New Economic Windows Series, Springer (2017)

- Anatoly V. Kondratenko.
*Physical Modeling of Economic Systems. Classical and Quantum Economies.*Novosibirsk, "Nauka" (2005),

### Lectures

- Economic Fluctuations and Statistical Physics: Quantifying Extremely Rare and Much Less Rare Events, Eugene Stanley, Videolectures.net

- Applications of Statistical Physics to Understanding Complex Systems, Eugene Stanley, Videolectures.net

- Financial Bubbles, Real Estate Bubbles, Derivative Bubbles, and the Financial and Economic Crisis, Didier Sornette, Videolectures.net

- Financial crises and risk management, Didier Sornette, Videolectures.net

- Bubble trouble: how physics can quantify stock-market crashes, Tobias Preis, Physics World Online Lecture Series

## External links

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类别: 应用和跨学科物理学

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类别: 数学金融

Category:Schools of economic thought

类别: 经济思想流派

Category:Statistical mechanics

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#### 经济物理学30年：物理学家能够拯救经济理论危机吗？

如今物理与经济的跨界交流正在发展，并且有希望在未来几年中得到有价值的突破，多主体模型或许能够成为经济学家和物理学家有所突破的共同基石。

This page was moved from wikipedia:en:Econophysics. Its edit history can be viewed at 经济物理学/edithistory