C. Quantum Theory and Social Sciences

By: Carlos Pedro Gonçalves

Talking about quantum theory to a social scientist usually leads to a stirring up of attention, never leaving people indifferent, this is also an experience that one may have in class, when mentioning two subject matters: chaos theory and quantum mechanics applications to social sciences.

About chaos theory students tend to state “Chaos?! Yes! Of course we know that!” the younger they are the more noise they tend to make about it, just feeling stimulated about the word “chaos” (more or less like a “giving caffeine to children” effect).

Regarding quantum mechanics, on the other hand, a wider variety of reactions take place, usually, however, in our personal experience, students tend to become serious, silent and thinking about it. Of course, if you mix the two in “quantum chaos” you get a mixture of reactions, the mention of the quantum usually leading to a concentrated serious gaze.

Chaos theory has been around for a while in the social sciences. Born as a branch of mathematics and physics, developed within nonlinear dynamics, it had a wealth of interdisciplinary contributions, besides mathematicians and physicists: economists, meteorologists, biologists, chemists, computer scientists, “complexologists”, and so on (Gleick, 1988).

Quantum theory’s application to social sciences, on the other hand, is a very recent but quickly growing field, in particular through econophysics. Quoting, on this regard, Saptsin and Soloviev (2009, p.2):

“Econophysics is a relatively new interdisciplinary scientific school, which tends to develop rapidly, having taken its shape and name in late 90-ies of the XX century. According to our estimation the number of original works and articles on the Internet, surveys and monographs has already exceeded thousands. Moreover respective courses and special subjects are being introduced in the high schools of far and near abroad.”

Encompassing both new theoretical foundations, grounded on complex systems sciences and risk science, as well as new notions, new scientific lexicon and methodological changes to the way one performs research in economics, econophysics is leading the research in economics to new areas and new paradigmatic bases, with robust empirical results.

The American Mathematical Society’s Mathematics Subject Classification “MSC2010” includes econophysics in the branch of “Game theory, economics, social and behavioral sciences” (91-XX) under the sub-branch of “Mathematical economics” (91Bxx) defining econophysics as:

“91B80 Applications of statistical and quantum mechanics to economics (econophysics).” (http://www.ams.org/mathscinet/msc/msc2010.html?t=&s=econophysics&btn=Search&ls=s)

The applications of quantum mechanics (including quantum statistical mechanics) to economics is called quantum econophysics.

Saptsin and Soloviev (2009) argue that quantum econophysics offers a research direction that goes beyond standard economics, providing contributions to complex systems sciences, in particular, regarding complex systems modeling, quoting (Saptsin and Soloviev, 2009, p.3):

“(…) In the contemporary comprehension complex systems are the problem in terms of formalization nonlinear systems, in the dynamics of which synergetic phenomena are observed, instabilities and poor predictability take place; the so-called aftereffect and “long memory” connected with it act the significant part. First of all socio-economical, ecological and other, which are similar to them and depict the upper levels of an integrated, organized and functioning in a complicated manner matter, can be related to such systems.”

This growing connection of quantum econophysics to complex systems sciences opens up the way for a new interdisciplinary research direction: the interdisciplinary expansion of complex quantum systems science (see Haken (1985) and NOTE 1) to general complex systems research, called quantum complex systems science, in which quantum econophysics and quantum risk science can be included as interdisciplinary intersections with, respectively, economics and risk science.

As of yet, quantum complex systems science is a nascent field still growing out of complex quantum systems science interdisciplinary expansions, in particular those developed within quantum econophysics.

There is, however, a major difference between the models developed within a standard quantum theory of games of strategy in comparison to a quantum theory of complex systems' dynamics. While single round games of strategy can be approached by a single Schrödinger wave dynamics, obeying some optimization scheme (quantum game equilibrium problem), a quantum theory of complex systems' dynamics has to deal with multiple round games.

The quantum econophysics of complex economic systems leads us away from the single Schrödinger equation and brings us to a disciplinary realm of quantum interacting field fluctuations, path dependent quantum computation, irreversibility, quantum chaos (both of the conservative and dissipative types), emerging hypercomputation, emerging classicality interacting and coevolving with the quantum substratum, quantum criticality.

Quantum coevolution becomes a major conceptual issue within this complex systems’ framework. Within complex quantum systems, quantum computation can proceed in a path dependent fashion, being capable of making emerge classical dynamics even without coarse-graining of histories or any other decoherence dynamics.

As proved by Gonçalves (2012), quantum computing structures can make emerge nonlinear dynamics, chaos and irreversibility at the sequence of quantum states while simultaneously conserving information in each computational step’s unitary transition. Following, Gonçalves (2012) quantum register machines, with a discrete alphabet, can make emerge both conservative and dissipative chaos at the single input level as well as at the quantum field computational level.

Once we consider the quantum field computational level, one can find examples of systems with the three dynamical phases of complex systems dynamics (Gonçalves, 2012): the regular, the chaotic and the intermediate called the edge of chaos (Langton, 1990; Crutchfield and Young, (1990); Kauffman, 1993), which in the quantum setting constitutes a quantum complex stochastic phase (Gonçalves, 2012).

Example of Quantum complex Stochastic Phase

One can also find, within a quantum computing field of a coupled quantum map lattice, emerging quantum dissipative structures (see NOTE 2) that exchange energy with field, feeding upon local energy fluctuations as well as upon other nearby structures, so that the quantum field becomes as a kind of primordial soup for emerging systemic individuations.

Example of Quantum Dissipative Structure

( For further details see: http://modelingcommons.org/browse/one_model/3436#model_tabs_browse_info )

Recently, quantum chaos and quantum field adaptive computation has been combined with quantum game theory to address the financial turbulence problem (see https://sites.google.com/site/quantumcomplexity/modeling-financial-turbulence for the follow-up on this matter).

NOTES:

NOTE 1:

The Brussels-Austin school has led to "The Center for Complex Quantum Systems", formerly known as "The Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems", focusing now on complex quantum systems science, the reference section of the center's web page http://order.ph.utexas.edu/ provides for various references on complex quantum systems. Another center is from the Synergetics school http://itp1.uni-stuttgart.de/en/.

Yet another interesting reference is http://www.nature.com/nphys/insight/quantum-simulation/index.html

A few other groups and centers working in complex quantum systems science are:

“Complex Quantum Systems Research Group” (http://www.physik.uni-regensburg.de/forschung/richter/richter/),

“The Dahlem Center for Complex Quantum Systems” (http://www.physik.fu-berlin.de/en/einrichtungen/dahlem_center_cqs/),

CoQus (http://www.coqus.at/).

NOTE 2:

A dissipative structure is an open system that feeds upon energy and matter from the environment, dissipating energy in its self-organizing systemic activity (Prigogine, 1962). The notion was introduced by Prigogine in his work on far-from-equilibrium thermodynamics, for which the author won the Nobel Prize in Chemistry in 1977.

Conceptually, the notion of dissipative structure synthesizes a dynamics of survival, linked to processes of (eco)systemic management to an adaptive sustainability in permanent game of aggregation and disaggregation.

REFERENCES:

[1] - Crutchfield, J. P. and Young, K. (1990). "Computation at the Onset of Chaos", in Entropy, Complexity, and the Physics of Information, Zurek, W. (Ed.), SFI Studies in the Sciences of Complexity, VIII, Addison-Wesley, Reading, USA, 223–269.

[2] - Haken, H. (1985). "Towards a Quantum Synergetics: Pattern Formation in Quantum Systems far from Thermal Equilibrium". Phys. Scr. 32 274.

[3] - Gleick, J. (1988). "Chaos: Making a New Science", USA, Penguin Books.

[3] - Gonçalves, C.P. (2012). "Quantum Chaos and Quantum Computing Structures", arXiv:1208.2610v1 [nlin.CD]

[4] - Gonçalves, C.P. (2012). "Financial Turbulence, Business Cycles and Intrinsic Time in an Artificial Economy". Algorithmic Finance (2012), 1:2, 141-156, http://algorithmicfinance.org/1-2/pp141-156/

[5] - Kauffman, S.A. (1993). "The Origins of Order: Self-Organization and Selection in Evolution". Oxford University Press, USA.

[6] - Langton, C. (1990). "Computation at the edge of chaos". Physica D, 42, 1990.

[7] - Prigogine, I. (1962), "Introduction to Thermodynamics of Irreversible Processes", USA, John Wiley and Sons.

[8] - Saptsin, V. and Soloviev, V. (2009). "Relativistic quantum econophysics - new paradigms in complex systems modelling". arXiv:0907.1142v1 [physics.soc-ph] .