Quantum Complex Systems Science, Risk Science and Econophysics

BY: Carlos Pedro Gonçalves

From the complex sciences’ scientific basis, quantum complex systems science may offer new conceptual and modeling tools to address risk in complex systems, including human societies and economies.

In order to be effective, quantum complex systems science must generalize formalisms, tools and methodologies to be able to apply them effectively in different settings. Thus, from the underlying formalism of quantum mechanics, one may develop interdisciplinary work and apply it to different problems which are of concern to the complex systems sciences and to risk science.

A few examples of research centers directly concerned with complex quantum systems include:

“The Center for Complex Quantum Systems” ( http://order.ph.utexas.edu/), 

“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/).

The above-quoted first research center works within the Brussels-Austin school for complexity, mainly influenced by Prigogine’s work and has a theoretical background that is strongly integrated with the conceptual basis of risk science.

Combining the Brussels-Austin approach with risk science, the dynamics of complex systems can be approached as a game of survival, such that complex systems need to expose themselves to risk situations, consuming resources and enacting adaptive dynamics towards the systemic sustainability, dynamics which are, themselves, generative of risk situations.

This conceptual basis for risk and complex systems’ dynamics results from the notion of  dissipative structure, introduced by Prigogine, within thermodynamics: a dissipative structure is an open system that feeds on energy and matter from the environment and dissipates heat as a way to sustain its systemic activity.

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

Combining the systemic thinking of Varela with Prigogine’s, one can address the notion of dissipative structure as a system whose autopoietic dynamics leads it to the survival far from a systemic regime of structural dissolution in a disaggregating flux (self-organization far from the thermodynamic equilibrium).

From the standpoint of risk science, a dissipative structure can be addressed in terms of a notion of risking structure, such that complex systems, worked from this notion, can be considered as enactors of systemic risk as an adaptive survival response when placed before permanent threats of disaggregating dissolution.

The dissipative structures/risking structures’ self-organizing processes constitute examples of adaptive processes related to a systemic struggle for survival, approached, within the Brussels-Austin School, from a notion of sustainability against a disaggregating flux, thus, these structures constitute examples of the notion of complex adaptive system, worked upon the Santa Fe Institute.

Quantum complex systems science can help address a general approach to risk and dynamics of complex adaptive systems whenever a mathematical approach is needed to incorporate the following elements:

a) Discrete state variables and continuous state averages with complex dynamical behavior (including (noisy) chaos);

b) Adaptive computation of risk;

c) Multiple intercoupled dynamics with different degrees of freedom;

d) Fluctuating population numbers;

e) Interacting adaptive fields on networks with quantized state variables.

The above elements make effective the usage of the mathematical formalism of quantum mechanics made available to interdisciplinary work through quantum game theory and, in the case of economics, through econophysics.

Application to Economics

In  the video below is an example of a model from a work that implements an application of quantum complex systems science and risk science to complex economic dynamics modeling.

The model, also available at Netlogo Commons (http://bit.ly/wyiWYc), is introduced in the article "Chaos and Nonlinear Dynamics in a Quantum Artificial Economy" arXiv:1202.6647v1 [nlin.CD] (http://arxiv.org/abs/1202.6647) and it constitutes an example of how quantum complex systems science can be applied to economics.

In most businesses, one deals with discrete business volumes (or in the case of companies that supply goods: discrete quantities), thus, to address economic chaotic dynamics one may, effectively, assume some quantization scheme of fundamental economic variables and economic equilibrium conditions, working with a business game process, in which the quantum averages, from transaction round to transaction roundm follow the continuous state classical chaotic dynamics of some (coupled) nonlinear map.

The work builds up on such a proposal, introducing a quantum artificial economy with (quantum) chaotic dynamics, by combining quantum game theory, quantum chaos theory and coherent state lattice field solutions.

At each transaction round, each company is characterized by a coherent state solution for the business volume (measured in quantities), which corresponds to a quantum business game equilibrium condition.

The nonlinear map introduces an adaptive walk on a hypercubic lattice, implementing a business' quantum economics version of Kaneko's self-organizing genetic algorithms. In this way, each company's binary string code corresponds to a core business strategic profile, where each bit of the binary string is a core business dimension (among core business dimensions one can include the mission statement and business concept).

The coupled quadratic map implements four types of evolutionary dynamics:

(A) - Local competition dynamics between companies that are close to each other in their core business strategic dimensions (local hypercubic lattice one-bit mutant neighors' coupling as per Kaneko's proposal of self-organizing genetic algorithms);

(B) - Global competitiveness' industry-wide evolutionary race;

(C) - Market share feedback effects upon a business fitness (this leads to a coupling between the quadratic map and the previous transaction round's company's market share, such that the previous round's quantum fluctuations affect the company's fitness dynamics).

(D) - Local fitness dynamics given by the quadratic map with nonlinearity parameter b.

Quantum chaos is a third approach to modeling economic nonlinear dynamics that can be added to the nonlinear deterministic and nonlinear deterministic plus noise modeling family of economic chaos. By addressing evolutionary quantum strategies one is not dealing with a plus noise approach but, instead, with an evolutionary systemic dynamics where probability distributions and chaotic dynamics are interconnected with risk cognition and business adaptive processes, thus, deepening the conceptual grounding on complex adaptive systems science and quantum complex systems science.