Econophysics is an 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.
2 Basic tools
4 Main results
5 See also
7 Further reading
8 External links
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 Prize in
economics 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
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.
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 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 almost regular meeting series on the topic include: APFA,
Econophysics Colloquium, 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
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.
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.
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, 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 the
of the Leiden University, from where the first Nobel-laureate
Jan Tinbergen came. From September 2014 King's College
has awarded the first position of Full Professor in Econophysics.
Basic tools of econophysics are probabilistic and statistical methods
often taken from statistical physics.
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.
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. 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 bounded 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. 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. 
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.
In a paper published in Physica A
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.
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.
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 economy and
quantum finance), and the path integral formulation of statistical
The concept of economic complexity index, introduced by the MIT
Cesar A. Hidalgo
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
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
Black-Scholes methodology). The
Black-Scholes theory can be
extended to provide an analytical theory of main factors in economic
Papers on econophysics have been published primarily in journals
devoted to physics and statistical mechanics, rather than in leading
economics journals. Mainstream economists have generally been
unimpressed by this work. Some economists, including Mauro
Gallegati, Steve Keen, Paul Ormerod, and Alan Kirman have shown more
interest, but also criticized some 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
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
neglegible 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
displaystyle Ppropto x^ -4 ,,
where x is an increasingly large variable in the tail region of the
distribution considered (i.e. a price statistics with much more than
108 data). I.e., the events considered are not simply "outliers" but
must really be taken into account and cannot be "insured
away". 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. The
"fat tails" are also observed in commodity markets.
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,
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.
Bose–Einstein condensation (network theory)
Potential Game (Bounded Rational)
Detrended fluctuation analysis
Kinetic exchange models of markets
^ Yale Economic Review, Retrieved October-25-09 Archived 2008-05-08 at
the Wayback Machine.
^ 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))
Econophysics of Wealth Distributions, Eds. A. Chatterjee, S.
Yarlagadda, B.K. Chakrabarti, New Economic Windows, Springer-Verlag,
^ 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)
Physics - Education". Physics.leidenuniv.nl. 2011–2013. Retrieved
2013. Check date values in: access-date= (help)
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2014. Check date values in: access-date= (help)
Physics - Education". Physics.leidenuniv.nl. 2011–2015. Retrieved
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^ Bikas K Chakrabarti, Anirban Chakraborti, Satya R Chakravarty, Arnab
Econophysics of Income & Wealth Distributions.
Cambridge University Press, Cambridge. CS1 maint: Multiple names:
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Didier Sornette (2003). Why Stock Markets Crash?. Princeton
^ Dixon, Huw (2000). "keeping up with the Joneses: competition and the
evolution of collusion". Journal of Economic Behavior and
Organization. 43: 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):
^ Zunino, L., Bariviera, A.F., Guercio, M.B., Martinez, L.B. and
Rosso, O.A. (2012). "On the efficiency of sovereign bond markets".
Physica A: Statistical
Mechanics and its Applications. 391 (18):
doi:10.1016/j.physa.2012.04.009. CS1 maint: Multiple names:
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^ 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". Journal of Statistical
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arXiv:1509.01839 . Bibcode:2013JSMTE..08..007F.
doi:10.1088/1742-5468/2013/08/P08007. CS1 maint: Multiple names:
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^ 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.
^ Anatoly V. Kondratenko (2015). Probabilstic Economic Theory. LAP
LAMBERT Academic Publishing. ISBN 978-3-659-89232-5.
^ a b Chen, Jing (2015). The Unity of Science and Economics: A New
Foundation of Economic Theory.
^ Ricardo Hausmann; Cesar Hidalgo; et al. "The Atlas of Economic
The Observatory of Economic Complexity
The Observatory of Economic Complexity (MIT Media Lab).
Retrieved 26 April 2012.
^ a b Jean-Philippe Bouchaud; Marc Potters (2003). Theory of Financial
Risk and Derivative Pricing.
Cambridge University Press.
^ Bouchaud, J-P.; Potters, M. (2001). "Welcome to a non-Black-Scholes
world". Quantitative Finance. 1: 482–483.
^ Philip Ball (2006). "Econophysics: Culture Crash". Nature. 441
(7094): 686–688. Bibcode:2006Natur.441..686B. doi:10.1038/441686a.
^ Enrico Scalas (2006). "The application of continuous-time random
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^ Y. Shapira; Y. Berman; E. Ben-Jacob (2014). "Modelling the short
term herding behaviour of stock markets". New Journal of Physics. 16:
^ Y. Liu; P. Gopikrishnan; P. Cizeau; M. Meyer; C.-K. Peng; H. E.
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^ M. H. R. Stanley; L. A. N. Amaral; S. V. Buldyrev; S. Havlin; H.
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^ K. Yamasaki; L. Muchnik; S. Havlin; A. Bunde; H.E. Stanley (2005).
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^ 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)
^ a b See for example Preis, Mantegna, 2003.
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 University Press (Cambridge, UK, 2004)
Bertrand Roehner, Patterns of Speculation - A Study in Observational
Cambridge University Press
Cambridge University Press (Cambridge, UK, 2002)
Surya Y., Situngkir, H., Dahlan, R. M., Hariadi, Y., Suroso, R.
(2004). Aplikasi Fisika dalam Analisis Keuangan (
in Financial Analysis. Bina Sumber Daya MIPA. ISBN 9793073527
Arnab Chatterjee, Sudhakar Yarlagadda, Bikas K Chakrabarti,
Econophysics of Wealth Distributions, Springer-Verlag Italia (Milan,
Philip Mirowski, More Heat than Light -
Economics as Social Physics,
Physics as Nature's Economics,
Cambridge University Press
Cambridge University Press (Cambridge,
Ubaldo Garibaldi and Enrico Scalas, Finitary Probabilistic Methods in
Cambridge University Press
Cambridge University Press (Cambridge, UK, 2010).
Emmanual Farjoun and Moshé Machover, Laws of Chaos: a probabilistic
approach to political economy, Verso (London, 1983) ISBN 0 86091
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 
A distribution function analysis of wealth distribution by Arnab Das
and Sudhakar Yarlagadda 
Analytical treatment of a trading market model by Arnab Das 
Martin Shubik and Eric Smith, The Guidance of an Enterprise Economy,
MIT Press,  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, , New Economic Windows Series,
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,
Bubble trouble: how physics can quantify stock-market crashes, Tobias
Physics World Online Lecture Series
Econophysics Colloquium 2017
Econophysics Ph.D. Program at University of Houston, Houston, TX.
Finance Gets Physical - Yale Economic Review
Conference to mark 25th anniversary of Farjoun and Machover's book
Chair of International Economics, University of Bamberg (Germany)
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