**Econophysics** is an interdisciplinary research field, applying theories and methods originally developed by

physicistsPhysics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

in order to solve problems in

economicsEconomics is the social science that analyzes the production, distribution, and consumption of goods and services. The term economics comes from the Ancient Greek from + , hence "rules of the house"...

, usually those including uncertainty or

stochastic processIn probability theory, a stochastic process , or sometimes random process, is the counterpart to a deterministic process...

es and

nonlinear dynamicsChaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

. Its application to the study of financial markets has also been termed

statistical financeStatistical finance, sometimes called econophysics, is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets...

referring to its roots in

statistical physicsStatistical physics is the branch of physics that uses methods of probability theory and statistics, and particularly the mathematical tools for dealing with large populations and approximations, in solving physical problems. It can describe a wide variety of fields with an inherently stochastic...

.

## History

Physicists’ interest in the

social sciencesSocial science is the field of study concerned with society. "Social science" is commonly used as an umbrella term to refer to a plurality of fields outside of the natural sciences usually exclusive of the administrative or managerial sciences...

is not new;

Daniel BernoulliDaniel Bernoulli was a Dutch-Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics...

, 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 FisherIrving Fisher was an American economist, inventor, and health campaigner, and one of the earliest American neoclassical economists, though his later work on debt deflation often regarded as belonging instead to the Post-Keynesian school.Fisher made important contributions to utility theory and...

, was originally trained under the renowned Yale

physicistA physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

,

Josiah Willard GibbsJosiah Willard Gibbs was an American theoretical physicist, chemist, and mathematician. He devised much of the theoretical foundation for chemical thermodynamics as well as physical chemistry. As a mathematician, he invented vector analysis . Yale University awarded Gibbs the first American Ph.D...

. Likewise,

Jan TinbergenJan Tinbergen , was a Dutch economist. He was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of economic processes...

, who won the first Nobel Prize in economics in 1969 for having developed and applied dynamic models for the analysis of economic processes, studied physics with

Paul EhrenfestPaul Ehrenfest was an Austrian and Dutch physicist, who made major contributions to the field of statistical mechanics and its relations with quantum mechanics, including the theory of phase transition and the Ehrenfest theorem.- Biography :Paul Ehrenfest was born and grew up in Vienna in a Jewish...

at

Leiden UniversityLeiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...

.

Econophysics was started in the mid-1990s by several physicists working in the subfield of

statistical mechanicsStatistical mechanics or statistical thermodynamicsThe terms statistical mechanics and statistical thermodynamics are used interchangeably...

. 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.

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.

The term “econophysics” was coined by

H. Eugene StanleyHarry Eugene Stanley is an American physicist and University Professor at Boston University. He has made seminal contributions to statistical physics and is one of the pioneers of interdisciplinary science...

in the mid 1990s, to describe the large number of papers written by physicists in the problems of (stock and other) markets, and first appeared in a conference on statistical physics in Calcutta in 1995 and its following publications. The inaugural meeting on Econophysics was organised 1998 in Budapest by

János KertészJános Kertész is a Hungarian physicist. He is one of the pioneers of econophysics, complex networks and application of fractal geometry in physical problems....

and Imre Kondor.

Currently, the almost regular meeting series on the topic include: Econophysics Colloquium, ESHIA/ WEHIA, ECONOPHYS-KOLKATA, APFA

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 Farjoun and Machover (1983). Their book

*Laws of Chaos: A Probabilistic Approach to Political Economy* proposes

*dis*solving (their words) the

transformation problemIn 20th century discussions of Karl Marx's economics the transformation problem is the problem of finding a general rule to transform the "values" of commodities into the "competitive prices" of the marketplace...

in Marx's political economy by re-conceptualising the relevant quantities as random variables.

If, on the other side, "econophysics" is taken to denote the application of physics to

economics, one can already consider the works of

Léon WalrasMarie-Esprit-Léon Walras was a French mathematical economist associated with the creation of the general equilibrium theory.-Life and career:...

and

Vilfredo ParetoVilfredo Federico Damaso Pareto , born Wilfried Fritz Pareto, was an Italian engineer, sociologist, economist, political scientist and philosopher. He made several important contributions to economics, particularly in the study of income distribution and in the analysis of individuals' choices....

as part of it. Indeed, as shown by Ingrao and Israel, general equilibrium theory in economics is based on the physical concept of

mechanical equilibriumA standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

.

Econophysics has nothing to do with the "physical quantities approach" to economics, advocated by Ian Steedman and others associated with

Neo-RicardianismThe neo-Ricardian school is an economic schoolthat derives from the close reading and interpretation of David Ricardo by Piero Sraffa, and from Sraffa's critique of Neoclassical economics as presented in his The Production of Commodities by Means of Commodities, and further developed by the...

. Notable econophysicists are

Jean-Philippe BouchaudJean-Philippe Bouchaud is a French physicist born in 1962. He is founder and Chairman of Capital Fund Management and professor of physics at École polytechnique.- Biography :...

,

Bikas K ChakrabartiBikas Kanta Chakrabarti is an Indian physicist.He is a professor of Physics at Saha Institute of Nuclear Physics, Kolkataand Visiting Professor of Economics, Indian Statistical Institute, Kolkata....

,

Dirk HelbingDirk Helbing is a physicist, and professor of sociology, in particular for modelling and simulation.- Biography :Dirk Helbing studied physics and mathematics at the University of Göttingen. He completed his doctoral thesis at Stuttgart University, on modeling social processes by means of...

,

János KertészJános Kertész is a Hungarian physicist. He is one of the pioneers of econophysics, complex networks and application of fractal geometry in physical problems....

, Matteo Marsili,

Joseph L. McCauleyJoseph L. McCauley, is Professor of Physics at the University of Houston. He was Lars Onsager's last graduate student. He is a keen hiker.His main research fields are economics and finance , nonlinear dynamics, and statistical physics...

, Enrico Scalas,

Didier SornetteDidier Sornette is Professor on the Chair of Entrepreneurial Risks at Swiss Federal Institute of Technology Zurich . He is also a professor of the Swiss Finance Institute, a professor associated with both the department of Physics and the department ofEarth Sciences at ETH Zurich, an Adjunct...

,

H. Eugene StanleyHarry Eugene Stanley is an American physicist and University Professor at Boston University. He has made seminal contributions to statistical physics and is one of the pioneers of interdisciplinary science...

, Victor Yakovenko and Yi-Cheng Zhang. Among the formal courses on Econophysics, that offered by the Physics Department of the

Leiden UniversityLeiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...

, from where the first Nobel-laureate in economics

Jan TinbergenJan Tinbergen , was a Dutch economist. He was awarded the first Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel in 1969, which he shared with Ragnar Frisch for having developed and applied dynamic models for the analysis of economic processes...

came,

is particularly noteworthy.

## Basic tools

Basic tools of econophysics are

probabilisticProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...

and

statisticalStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....

methods often taken from statistical physics.

Physics models that have been applied in economics include

percolationIn physics, chemistry and materials science, percolation concerns the movement and filtering of fluids through porous materials...

models,

chaoticChaos theory is a field of study in mathematics, with applications in several disciplines including physics, economics, biology, and philosophy. Chaos theory studies the behavior of dynamical systems that are highly sensitive to initial conditions, an effect which is popularly referred to as the...

models developed to study cardiac arrest, and models with self-organizing criticality as well as other models developed for

earthquake predictionAn earthquake prediction is a prediction that an earthquake of a specific magnitude will occur in a particular place at a particular time . Despite considerable research efforts by seismologists, scientifically reproducible predictions cannot yet be made to a specific day or month...

. Moreover, there have been attempts to use the mathematical theory of

complexityIn general usage, complexity tends to be used to characterize something with many parts in intricate arrangement. The study of these complex linkages is the main goal of complex systems theory. In science there are at this time a number of approaches to characterizing complexity, many of which are...

and

information theoryInformation theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

, as developed by many scientists among whom are

Murray Gell-MannMurray Gell-Mann is an American physicist and linguist who received the 1969 Nobel Prize in physics for his work on the theory of elementary particles...

and Claude E. Shannon, respectively.

Since economic phenomena are the result of the interaction among many heterogeneous

agentsIn economics, an agent is an actor and decision maker in a model. Typically, every agent makes decisions by solving a well or ill defined optimization/choice problem. The term agent can also be seen as equivalent to player in game theory....

, there is an analogy with statistical mechanics, where many particles interact; but it must be taken into account that the properties of human beings and particles significantly differ.

Another good example is Random Matrix Theory, which can be used to identify the noise in financial correlation matrices. It has been shown that this technique can significantly improve the performance of portfolios, e.g., in applied in

Portfolio OptimizationModern portfolio theory is a theory of investment which attempts to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets...

. Thus, this practice is commonly encountered in the praxis of quantitative finance.

There are, however, various other tools from physics that have so far been used with mixed success, such as

fluid dynamicsIn physics, fluid dynamics is a sub-discipline of fluid mechanics that deals with fluid flow—the natural science of fluids in motion. It has several subdisciplines itself, including aerodynamics and hydrodynamics...

,

classical mechanicsIn physics, classical mechanics is one of the two major sub-fields of mechanics, which is concerned with the set of physical laws describing the motion of bodies under the action of a system of forces...

and

quantum mechanicsQuantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

(including so-called classical economy, quantum economy and

quantum financeQuantum finance is an interdisciplinary research field, applying theories and methods developed by quantum physicists and economists in order to solve problems in finance. It is a type of Econophysics.- Background on instrument pricing:...

), and the

path integral formulationThe path integral formulation of quantum mechanics is a description of quantum theory which generalizes the action principle of classical mechanics...

of statistical mechanics.

There are also analogies between finance theory and

diffusionMolecular diffusion, often called simply diffusion, is the thermal motion of all particles at temperatures above absolute zero. The rate of this movement is a function of temperature, viscosity of the fluid and the size of the particles...

theory. For instance, the Black-Scholes equation for

optionIn finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the...

pricing is a

diffusion-

advectionAdvection, in chemistry, engineering and earth sciences, is a transport mechanism of a substance, or a conserved property, by a fluid, due to the fluid's bulk motion in a particular direction. An example of advection is the transport of pollutants or silt in a river. The motion of the water carries...

equation.

## Impact on mainstream economics and finance

Papers on econophysics have been published primarily in journals devoted to physics and statistical mechanics, rather than in leading economics journals.

Mainstream economistsMainstream economics is a loose term used to refer to widely-accepted economics as taught in prominent universities and in contrast to heterodox economics...

have generally been unimpressed by this work. Some

Heterodox economists"Heterodox economics" refers to approaches or to schools of economic thought that are considered outside of "mainstream economics". Mainstream economists sometimes assert that it has little or no influence on the vast majority of academic economists in the English speaking world. "Mainstream...

, including Mauro Gallegati,

Steve KeenSteve Keen is a Professor in economics and finance at the University of Western Sydney. He classes himself as a post-Keynesian, criticizing both modern neoclassical economics and Marxian economics as inconsistent, unscientific and empirically unsupported...

and

Paul OrmerodPaul Ormerod is a Lancastrian economist who is currently researching complexity, complex systems, nonlinear feedback, the boom and bust cycle of business and economic competition...

, have shown more interest, but also criticized trends in econophysics.

In contrast, econophysics is having some impact 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 financial markets or original points of view on established models. Also several scaling laws have been found in various economic data.

## See also

- Bose–Einstein condensation (network theory)
- Complexity economics
Complexity economics is the application of complexity science to the problems of economics. It studies computer simulations to gain insight into economic dynamics, and avoids the assumption that the economy is a system in equilibrium.- Models :...

- Complex network
In the context of network theory, a complex network is a graph with non-trivial topological features—features that do not occur in simple networks such as lattices or random graphs but often occur in real graphs...

- Detrended fluctuation analysis
In stochastic processes, chaos theory and time series analysis, detrended fluctuation analysis is a method for determining the statistical self-affinity of a signal. It is useful for analysing time series that appear to be long-memory processes In stochastic processes, chaos theory and time series...

- Kinetic exchange models of markets
Kinetic exchange models are multi-agent dynamic models inspired by the statistical physics of energy distribution, which try to explain the robust and universal features of income/wealth distributions....

- Long-range dependency
Long-range dependency is a phenomenon that may arise in the analysis of spatial or time series data. It relates to the rate of decay of statistical dependence, with the implication that this decays more slowly than an exponential decay, typically a power-like decay...

- Network theory
Network theory is an area of computer science and network science and part of graph theory. It has application in many disciplines including statistical physics, particle physics, computer science, biology, economics, operations research, and sociology...

- Network science
Network science is a new and emerging scientific discipline that examines the interconnections among diverse physical or engineered networks, information networks, biological networks, cognitive and semantic networks, and social networks. This field of science seeks to discover common principles,...

- Thermoeconomics
Thermoeconomics, also referred to as biophysical economics, is a school of heterodox economics that applies the laws of thermodynamics to economic theory. The term "thermoeconomics" was coined in 1962 by American engineer Myron Tribus, and developed by the statistician and economist Nicholas...

### Textbooks

- Rosario N. Mantegna, H. Eugene Stanley
Harry Eugene Stanley is an American physicist and University Professor at Boston University. He has made seminal contributions to statistical physics and is one of the pioneers of interdisciplinary science...

, *An Introduction to Econophysics: Correlations and Complexity in Finance*, Cambridge University Press (Cambridge, 1999)
- Vladimir N Pokrovskii,
*Econodynamics. The Theory of Social Production*, Springer: Berlin (2011).
- Nicholas Georgescu-Roegen
Nicholas Georgescu-Roegen, born Nicolae Georgescu was a Romanian mathematician, statistician and economist, best known for his 1971 magnum opus The Entropy Law and the Economic Process, which situated the view that the second law of thermodynamics, i.e., that usable "free energy" tends to disperse...

, The Entropy Law and the Economic Process, Harvard University Press: Cambridge, Massachusetts, 1971.
- Johannes Voit,
*The Statistical Mechanics of Financial Markets*, Springer; 3rd edition (Berlin 2005)
- Sitabhra Sinha, Arnab Chatterjee, Anirban Chakraborti, Bikas K Chakrabarti
Bikas Kanta Chakrabarti is an Indian physicist.He is a professor of Physics at Saha Institute of Nuclear Physics, Kolkataand Visiting Professor of Economics, Indian Statistical Institute, Kolkata....

. *Econophysics: An Introduction*, Wiley-VCH (2010)
- Jean-Philippe Bouchaud
Jean-Philippe Bouchaud is a French physicist born in 1962. He is founder and Chairman of Capital Fund Management and professor of physics at École polytechnique.- Biography :...

, Marc Potters, * Theory of Financial Risk and Derivative Pricing*, Cambridge University Press (2003)
- Bikas K Chakrabarti
Bikas Kanta Chakrabarti is an Indian physicist.He is a professor of Physics at Saha Institute of Nuclear Physics, Kolkataand Visiting Professor of Economics, Indian Statistical Institute, Kolkata....

, 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, 2004)
- Bertrand Roehner,
*Patterns of Speculation - A Study in Observational Econophysics*, Cambridge University Press (Cambridge, 2002)
- Arnab Chatterjee, Sudhakar Yarlagadda, Bikas K Chakrabarti
Bikas Kanta Chakrabarti is an Indian physicist.He is a professor of Physics at Saha Institute of Nuclear Physics, Kolkataand Visiting Professor of Economics, Indian Statistical Institute, Kolkata....

, *Econophysics of Wealth Distributions*, Springer-Verlag Italia (Milan, 2005)
- Keith Meyer,
*Extending and simulating the quantum binomial options pricing model*, University of Manitoba (Winnipeg, 2009)
- Hagen Kleinert
Hagen Kleinert is Professor of Theoretical Physics at the Free University of Berlin, Germany , at theWest University of Timişoara, at thein Bishkek. He is also of the...

, *Path Integrals in Quantum Mechanics, Statistics, Polymer Physics, and Financial Markets*, 3rd edition, World Scientific (Singapore, 2004) also available online on physik.fu-berlin.de
- Emmanuel Farjoun and Moshe Machover,
*Laws of Chaos; A Probabilistic Approach to Political Economy*, London: Verso, 1983. Probabilisticpoliticaleconomy.net
- Philip Mirowski
Philip Mirowski is a historian and philosopher of economic thought at the University of Notre Dame. He received a PhD in Economics from the University of Michigan in 1979.-Career:...

, *More Heat than Light - Economics as Social Physics, Physics as Nature's Economics*, Cambridge University Press (Cambridge, UK, 1989)
- Bruna Ingrao and Giorgio Israel,
*The Invisible Hand - Economic Equilibrium in the History of Science*, The MIT Press (Cambridge, MA, 1990).
- Didier Sornette
Didier Sornette is Professor on the Chair of Entrepreneurial Risks at Swiss Federal Institute of Technology Zurich . He is also a professor of the Swiss Finance Institute, a professor associated with both the department of Physics and the department ofEarth Sciences at ETH Zurich, an Adjunct...

, *Why Stock Markets Crash: Critical Events in Complex Financial Systems*, Princeton University Press (2004).
- Giovanni Naldi, Lorenzo Pareschi, Giuseppe Toscani,
*Mathematical modelling of collective behavior in socio-economic and life sciences*, Birkhauser, (2010).
- Reiner Kümmel,
*The Second Law of Economics: Energy, Entropy, and the Origins of Wealth*, Springer: Berlin (2011).

### Journal articles, PhD theses

- Mauro Gallegati, Steve Keen, Thomas Lux and Paul Ormerod,
*Worrying Trends in Econophysics*, Physica A **370**, 1-6 (2006).
- Special issue of the Journal of Economic Dynamics and Control
The Journal of Economic Dynamics and Control is a peer-reviewed scholarly journal devoted to computational economics, dynamic economic models, and macroeconomics. It is edited at the University of Amsterdam and published by Elsevier...

, January 2008: 'Applications of statistical physics in economics and finance'.
- W.K. Bertram
Dr William Karel Bertram is an Australian mathematician specializing in the fields of stochastic processes and econophysics.-Biography:...

, *Modelling asset dynamics via an empirical investigation of Australian Stock Exchange data*, PhD Thesis (2005).
- Special issue of 'SCIENCE AND CULTURE', September–October 2010, Volume 76, N.9-10 'On 15 Years of Econophysics Research'.

## Lectures

- Economic Fluctuations and Statistical Physics: Quantifying Extremely Rare and Much Less Rare Events, Eugene Stanley, Vicedolectures.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
Didier Sornette is Professor on the Chair of Entrepreneurial Risks at Swiss Federal Institute of Technology Zurich . He is also a professor of the Swiss Finance Institute, a professor associated with both the department of Physics and the department ofEarth Sciences at ETH Zurich, an Adjunct...

, Videolectures.net
- Financial crises and risk management, Didier Sornette
Didier Sornette is Professor on the Chair of Entrepreneurial Risks at Swiss Federal Institute of Technology Zurich . He is also a professor of the Swiss Finance Institute, a professor associated with both the department of Physics and the department ofEarth Sciences at ETH Zurich, an Adjunct...

, Videolectures.net
- Bubble trouble: how physics can quantify stock-market crashes, Tobias Preis
Tobias Preis is a German physicist and founder of the Artemis Capital Asset Management GmbH. Born in Limburg an der Lahn, Germany, he researches complex systems with H. Eugene Stanley at Boston University and Dirk Helbing at ETH Zurich. He was awarded a Ph.D...

, Physics World Online Lecture Series

## External links