arXiv subjects

Georgi Yordanov Georgiev

Publications and source records attributed to Georgi Yordanov Georgiev.

7 recordsLinked to original sources

arXiv2026

Exact Evolution Law for Action-Weighted Path Ensembles and the Dynamics of Self-Organization

Self-organizing open systems sustained by source--sink fluxes transform stochastic motion into ordered behavior, yet a general dynamical criterion governing this process has not been established. This paper derives an exact kinematic law for evolving action-weighted canonical path ensembles, and decomposes the dynamics of the ensemble-average action. In the precision-driven regime, the evolution closes: the rate of change is governed by the action variance, so increasing selectivity concentrates probability weight toward lower-action trajectories, causing the average action to decrease monotonically and behave as a Lyapunov-type quantity. Constant and decreasing selectivity lead to stationary and broadening behavior. Endogenous reduction of the average action defines self-organization, while externally prescribed modulation defines controlled ensemble evolution. The framework further admits system-dependent realizations of selectivity dynamics, including reconstruction from observable statistics and feedback-driven evolution, without modifying the underlying kinematic law. By using stochastic action as the organizing trajectory-level quantity, the approach connects path-ensemble organization to stochastic least-action ordering while yielding measurable diagnostics, finite-time constraints, and falsifiable signatures in open stochastic systems.

nlin.AO↗

arXiv2024

Why and How do Complex Systems Self-Organize at All? Average Action Efficiency as a Predictor, Measure, Driver, and Mechanism of Self-Organization

Self-organization in complex systems is a process in which randomness is reduced and emergent structures appear that allow the system to function in a more competitive way with other states of the system or with other systems. It occurs only in the presence of energy gradients, facilitating energy transmission through the system and entropy production. Being a dynamic process, self-organization requires a dynamic measure and dynamic principles. The principles of decreasing unit action and increasing total action are two dynamic variational principles that are viable to utilize in a self-organizing system. Based on this, average action efficiency can serve as a quantitative measure of the degree of self-organization. Positive feedback loops connect this measure with all other characteristics of a complex system, providing all of them with a mechanism for exponential growth, and indicating power law relationships between each of them as confirmed by data and simulations. In this study, we apply those principles and the model to agent-based simulations. We find that those principles explain self-organization well and that the results confirm the model. By measuring action efficiency we can have a new answer to the question: "What is complexity and how complex is a system?". This work shows the explanatory and predictive power of those models, which can help understand and design better complex systems.

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arXiv2022

Self-Organization In Stellar Evolution: Size-Complexity Rule

Complexity Theory is highly interdisciplinary, therefore any regularities must hold on all levels of organization, independent on the nature of the system. An open question in science is how complex systems self-organize to produce emergent structures and properties, a branch of non-equilibrium thermodynamics. It has long been known that there is a quantity-quality transition in natural systems. This is to say that the properties of a system depend on its size. More recently, this has been termed the size-complexity rule, which means that to increase their size, systems must increase their complexity, and that to increase their complexity they must grow in size. This rule goes under different names in different disciplines and systems of different nature, such as the area-speciation rule, economies of scale, scaling relations (allometric) in biology and for cities, and many others. We apply the size-complexity rule to stars to compare them with other complex systems in order to find universal patterns of self-organization independent of the substrate. Here, as a measure of complexity of a star, we are using the degree of grouping of nucleons into atoms, which reduces nucleon entropy, increases the variety of elements, and changes the structure of the star. As seen in our previous work, complexity, using action efficiency, is in power law proportionality of all other characteristics of a complex system, including its size. Here we find that, as for the other systems studied, the complexity of stars is in a power law proportionality with their size - the bigger a system is, the higher its level of complexity is - despite differing explosion energies and initial metallicities from simulations and data, which confirms the size-complexity rule and our model.

astro-ph.SR↗

arXiv2015

Free Energy Rate Density and Self-organization in Complex Systems

One of the most important tasks in science is to understand the self-organization's arrow of time. To attempt this we utilize the connection between self-organization and non-equilibrium thermodynamics. Eric Chaisson calculated an exponential increase of Free Energy Rate Density (FERD) in Cosmic Evolution, from the Big Bang until now, paralleling the increase of system's structure. We term these studies "Devology". We connect FERD to the principle of least action for complex systems, driving their increase of action efficiency. We study CPUs as a specific system in which the organization, the total amount of action and FERD are connected in a positive feedback loop, providing exponential growth of all three and power law relations between them. This is a deep connection, reaching to the first principles of physics: the least action principle and the second law of thermodynamics. We propose size-density and complexity-density rules in addition to the established size-complexity one.

nlin.AO↗

arXiv2014

Mechanism of organization increase in complex systems

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.

nlin.AO↗

arXiv2013

A quantitative measure, mechanism and attractor for self-organization in networked complex systems

Quantity of organization in complex networks here is measured as the inverse of the average sum of physical actions of all elements per unit motion multiplied by the Planck's constant. The meaning of quantity of organization is the inverse of the number of quanta of action per one unit motion of an element. This definition can be applied to the organization of any complex system. Systems self-organize to decrease the average action per element per unit motion. This lowest action state is the attractor for the continuous self-organization and evolution of a dynamical complex system. Constraints increase this average action and constraint minimization by the elements is a basic mechanism for action minimization. Increase of quantity of elements in a network, leads to faster constraint minimization through grouping, decrease of average action per element and motion and therefore accelerated rate of self-organization. Progressive development, as self-organization, is a process of minimization of action.

nlin.AO↗

arXiv2013

Increase of Organization in Complex Systems

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.

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