Mechanism of organization increase in complex systems

Abstract

This paper proposes a variational approach to describe the evolution of organization of complex systems from first principles, as increased efficiency of physical action. Most simply stated, physical action is the product of the energy and time necessary for motion. When complex systems are modeled as flow networks, this efficiency is defined as a decrease of action for one element to cross between two nodes, or endpoints of motion - a principle of least unit action. We find a connection with another principle that of most total action, or a tendency for increase of the total action of a system. This increase provides more energy and time for minimization of the constraints to motion in order to decrease unit action, and therefore to increase organization. Also, with the decrease of unit action in a system, its capacity for total amount of action increases. We present a model of positive feedback between action efficiency and the total amount of action in a complex system, based on a system of ordinary differential equations, which leads to an exponential growth with time of each and a power law relation between the two. We present an agreement of our model with data for core processing units of computers. This approach can help to describe, measure, manage, design and predict future behavior of complex systems to achieve the highest rates of self-organization and robustness.Comment: 22 pages, 4 figures, 1 tabl

Noise induced phase transition between maximum entropy production structures and minimum entropy production structures?

“…In contrast, in dissipative systems without an energy source the potential energy is minimized at stationary states. Since its appearance, Prigogine's principle of minimum entropy production has stimulated a lot of critical discussions [6][7][8][9][10][11][12], including Ziegler's conclusion, that entropy production is maximized in nonequilibrium systems [13][14][15][16][17][18]. Several authors suggested that the entropy production is neither maximal nor minimal [19,20].…”

Is the statement of Murphy's law valid?

“…The flow of energy during any arbitrary process when coupled with the dimension of time gives rise to the notion of action , formally represented as , where the pair, is the generalized position‐momentum pair, t is the time, δE is the change in energy along a specific path (in this case ), T and V are the kinetic and potential energies, respectively, and , the Lagrangian . There are several interpretations of the Action Principle, for example, the laws of physics when formulated in terms of the Action Principle identify any natural process as the one in which energy differences are leveled off in the least possible time (Maupertius' formulation) ; among all existing possible paths, the path of least action is the one along which a natural process must proceed (Hamiltonian formulation) (Chatterjee, submitted). On the energy landscape, there is a unique trajectory that directs (energy) flows along the lines of steepest descent.…”

Morphogenesis as Bayesian inference: A variational approach to pattern formation and control in complex biological systems

“…In (dissipative) random dynamical systems [Arnold, 1995], [Crauel and Flandoli, 1994], action is not minimized for each element of the system, but, on average over an ensemble of elements (or repeated trajectories of the same element) [Georgiev and Georgiev, 2002], [Georgiev et al, 2015], [Georgiev and Chatterjee, 2016], [Georgiev et al, 2017]. Obstructive-constraint minimization therefore reduces action for each event within the system and self-organizes it, forming a flow structure that could be construed as a dissipative structure [England, 2015], [Evans and Searles, 2002], [Prigogine, 1978].…”