Alexander Casey | Searcharxiv

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.

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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.

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