Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31903
Increase of Organization in Complex Systems

Authors: Georgi Yordanov Georgiev, Michael Daly, Erin Gombos, Amrit Vinod, Gajinder Hoonjan


Measures of complexity and entropy have not converged to a single quantitative description of levels of organization of complex systems. The need for such a measure is increasingly necessary in all disciplines studying complex systems. To address this problem, starting from the most fundamental principle in Physics, here a new measure for quantity of organization and rate of self-organization in complex systems based on the principle of least (stationary) action is applied to a model system - the central processing unit (CPU) of computers. The quantity of organization for several generations of CPUs shows a double exponential rate of change of organization with time. The exact functional dependence has a fine, S-shaped structure, revealing some of the mechanisms of self-organization. The principle of least action helps to explain the mechanism of increase of organization through quantity accumulation and constraint and curvature minimization with an attractor, the least average sum of actions of all elements and for all motions. This approach can help describe, quantify, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self organization to improve their quality. It can be applied to other complex systems from Physics, Chemistry, Biology, Ecology, Economics, Cities, network theory and others where complex systems are present.

Keywords: Organization, self-organization, complex system, complexification, quantitative measure, principle of least action, principle of stationary action, attractor, progressive development, acceleration, stochastic.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1491


[1] G. Y. Georgiev "A quantitative measure, mechanism and attractor for self-organization in networked complex systems", in Lecture Notes in Computer Science (LNCS 7166), F.A. Kuipers and P.E. Heegaard (Eds.): IFIP International Federation for Information Processing, Proceedings of the Sixth International Workshop on Self-Organizing Systems (IWSOS 2012), pp. 90-95, Springer- Verlag (2012).
[2] G. Georgiev, I. Georgiev, "The least action and the metric of an organized system." Open Syst. Inf. Dyn. 9(4), 371 (2002)
[3] P. de Maupertuis, Essai de cosmologie. (1750)
[4] D. A. Hoskins, "A least action approach to collective behavior." in Proc. SPIE, Microrob. and Micromech. Syst. 2593, L. E. Parker, Ed. 108-120 (1995)
[5] O. Piller, B. Bremond, M. Poulton, "Least Action Principles Appropriate to Pressure Driven Models of Pipe Networks." ASCE Conf. Proc. 113 (2003)
[6] L. Willard, A. Miranker, "Neural network wave formalism." Adv. in Appl. Math. 37(1), 19-30 (2006)
[7] J. Wang, K. Zhang, E. Wang, "Kinetic paths, time scale, and underlying landscapes: A path integral framework to study global natures of nonequilibrium systems and networks." J. Chem. Phys. 133, 125103 (2010)
[8] A. Annila, S. Salthe "Physical foundations of evolutionary theory." J. Non-Equilib. Thermodyn. 301-321 (2010)
[9] T. C. Devezas, "Evolutionary theory of technological change: State-of-the-art and new approaches." Tech. Forec. & Soc. Change 72 1137-1152 (2005)
[10] E. J. Chaisson, The cosmic Evolution. Harvard (2001)
[11] Y. Bar-Yam, Dynamics of Complex Systems. Addison Wesley (1997)
[12] J. M. Smart, "Answering the Fermi Paradox." J. of Evol. and Tech. June (2002)
[13] C. Vidal, "Computational and Biological Analogies for Understanding Fine-Tuned Parameters in Physics." Found. of Sci. 15(4), 375-393 (2010)
[14] C. Gershenson, F. Heylighen, "When Can We Call a System Self- Organizing?" Lect. Notes in Comp. Sci. 2801, 606-614 (2003).