In Complex Systems the collective behavior of the parts entails emergence of properties that can hardly, if at all, be inferred from properties of the parts. Science of Complex Systems provides radical new ways of understanding the physical, biological, ecological, and social universe. It helps reducing the gap between pure and applied science, establishing new foundations for the design, management and control of systems with levels of complexity exceeding the capacity of current approaches. Our approach is using efficiency as a measure of the extent to which input is well used for an intended task or function (output), and is often measured as the ratio of useful output to total input. Of course efficiency in complex systems refers to very different inputs and outputs in different fields.
Physical complex systems are open systems out of thermal equilibrium obeying the second law of thermodynamics and the principle of least action at the same time. To achieve maximum energy dispersal in order to increase entropy in the environment, they self-organize to provide flow network of channels for the energy flow through them. This flow network ensures the increasing efficiency in energy transmission through the system, as it evolves. Systems that are more efficient in energy dispersal, outcompete the less efficient ones for evolutionary survival. Biological and social systems are also complex systems, and there the efficiency of the system we define as the ratio of number of events: metabolic reactions, economic transactions, information transmitted through language, vs. the product of time and energy (action) that they consume. Therefore we define the level of organization of a system as the reciprocal of the average action efficiency for one event. This can be expressed as power, space, time and other form of efficiency in evolving complex systems. We are looking for a common framework to trace the increase of efficiency as a measure for level of organization and evolutionary stage of complex systems.
Moreover, approaching efficiency in complex systems in terms of simplicity, Murray Gell-Mann, physicist, raises the question: "In the description of nature, does deep simplicity always underlie apparent surface complexity?" Trying to use a definition for what might be simple or complex, Chaitin and Kolmogorov, mathematicians, described it as the minimum length of a message describing a system up to a given level of detail to a distant observer using a given grammar and vocabulary. However, there are usually different levels of description and at each level there are patterns that give the appropriate laws for that level. It is among those laws that one tends to find opportunities for practical reduction to more basic levels, with deep simplicity explaining away a great deal of the surface complexity.
Contributions from all disciplines that provide data for the increase of efficiency in the evolution of complex systems will move the field closer to the goal of creating a universal understanding of self-organization.
On the origin of universal patterns
Complex systems display at all scales skewed distributions, spirals and sigmoid curves which comply closely with lognormal or power law distributions. Moreover, oscillations and chaotic behavior are not random either but share the same characteristics independent of scale. Common patterns imply a universal law. Laws in turn are found by recognizing a phenomenon that is common and mathematizing an example of it. So, what is common to all systems that evolve to complexity? It is evolution itself, that is, change. In terms of physics a change takes place when a quantum moves from surroundings to the system, or vice versa. For example, the quantum of light carries energy and time, and hence evolution steps forward in terms of energy and time toward balance. The general equation of evolution can be formulated by inspecting an energy level diagram of a system. The system´s state can be given in terms of probability as pioneered by Boltzmann and Gibbs, however, including quanta of light from surroundings. This leads to statistical mechanics of open quantized systems. Subsequently logarithm of the state equation gives entropy whose rate of change is the evolutionary equation known as the 2nd law of thermodynamics. When the equation is analyzed, it is found to results in the ubiquitous patterns. Perhaps more intriguing, the evolutionary equation yields non-determinate history.
Constructal Law: Life and Evolution as Physics
What is evolution and why does it exist in the geophysical, biological, social and technological realms – in short, everywhere? Why is there a time direction – a time arrow – in the changes we know are happening every moment and everywhere? These are questions of physics, about everything. The physics answer is that nothing lives, flows, moves and morphs unless it is driven by power and has freedom to change. The power is destroyed by the flows, and the flow architectures evolve into configurations that provide progressively greater access for movement. The universal natural tendency to ‘evolve’ was placed in physics by the constructal law (1996). In this lecture I show why this law is useful to us. We are the evolving “human & machine species.” Evolution can be put to use in our lifetime in technology, transportation, urban design, spreading and collecting, miniaturization, communications, science, government and the unstoppable march to freedom, access, wealth and knowledge.
The lecture is based on the book: THE PHYSICS OF LIFE: The Evolution of Everything
(St. Martin’s Press, New York, 2016).
Efficiency of Energy Transfer in Rayleigh-Benard Convection
Sean McGrath, Yash Yadati, Atanu Chatterjee, Georgi Georgiev, Germano Iannacchione
The study of self-organization of complex systems has been a significant importance to the scientific community for a while now. Self-organization can be defined as a spontaneous formation of an ordered pattern from complete disorder due to local interactions and energy flows. These patterns are formed in various systems throughout nature. One of the more recognizable patterns are the formation of Rayleigh-Benard Convection cells. When a liquid is evenly heated from the bottom and evenly cooled from its surface the liquid tends to self-organize into successively more efficient patterns, such as rolls and hexagonal cells, with an upward flow of the hotter liquid from the bottom, and a downward flow of the cooler liquid from the top. In our experiments, we use a thermocouple that is attached to a copper plate and an infrared camera that is positioned directly above the plate to measure the temperatures of the hotter and colder fluid. A heater is attached to the bottom of the copper plate and voltages of 10V-80V is introduced to heat the working fluid. The fluid we use is Silicone oil with varying viscosities (5cst,10cst,150cst) and varying thicknesses (50mm-300mm). Using ImageJ software we analyze the thermal profile of each one of these experiments and calculate the entropy, dissipation of heat and the work done on the sample during convection which will give us the action efficiency of the energy transmission through each pattern. The principle of least action leads to self-organization for maximum action efficiency. The working hypothesis is that the energy rate density increases with increased action efficiency in the system, up to a limit. The nature of the dependency is the goal of this study. These results are compared to similar findings about this dependency in other physical systems in search for universality.
New Approach on Analyzing Trends in Evolving Computer Architecture
Noor Kawmi, Atanu Chatterjee, Georgi Georgiev and Germano S. Iannacchione
In this paper, we present a new way of analyzing the CPU data in order to study trends in technological evolution. We analyze the existing data using nonlinear regression methods. In the light of our analysis we observed that the data follows two different trends. Such an insight was absent from the empirical analysis in our previous papers, and also the existing literature.The empirical analysis was carried out by using log-transformed data points on a linear scale. Our aim is to find whether the Principle of Stationary Action apply to artificial systems despite human intervention. This was done by plotting different, direct and derived, parameters for a wide array of CPU architectures, and looking for trends in the graphs. For easy visualization of the graphs, the raw data points were plotted on a logarithmic scale. We found out that points on most of the graphs do not fit into a single fit-line. In fact, those points seemed to change slope around a certain region that corresponds to the introduction of the Pentium generation of the CPU models in the year, 1994. Thus, the nonlinear regression model fits the points with two different allometric fits having two different slopes. Moreover, we found that the most frequent action generated by all CPUs analysed in our study is the lowest in value which corresponds to the Principle of Least Action. In addition, we notice that entropy follows a decreasing trend with increasing efficiency, but an increasing trend with increasing power across the different generations of CPU studied. Keywords: Principle of Least Action, Nonlinear fitting, Allometric fits, Entropy, Statistical analysis.
Efficiency of Quranic Grammar for Modelling DNA Structures
Mahmoud Shokrollahi-Far and Peyman Passban
Formal Grammars, as finite sets of production rules to form structurally correct constituents of a language from its basic elements, originally emerged trying to employ a mathematical representation to model structures of natural languages. Now they are also employed to model mathematically any sequential system other than natural languages such as DNA sequences. However, the grammars employed have been effective in modelling just the coding sections of DNA sequences comprising only 2% to 5% of the molecule, leaving the rest 98% to 95% of the molecule ‘non-coding’. Moreover, these grammars are commonly complex in the sense that they impose costly computational overheads. Accordingly, more interesting would be less complex grammars which model the maximum number phenomena using simpler and less number of rules, hence more efficient. Our studies demonstrate that Quranic grammar developed on Quranic structural constituents, here called MOBIN Grammar, has the reliable grammatical properties for modeling DNA shuffling structures. In other words, this grammar that is at the least complex level in Chomsky Hierarchy of Formal Grammars provides a very efficient set of rules with the minimum length and the maximum coverage for modelling DNA shuffling structures very effectively.
Action efficiency as the criterion for the most organized state and the attractor of progressive development
Action efficiency stemming from the principle of least action is the natural state motion. All motions in nature happen with the least possible amount of action, which is the product of time and energy. In complex systems, due to the interaction of all agents, their paths are changed, but the basic physics principle of least action still holds, leading to a structure that minimizes action for each agent as much as possible. When two systems are compared, the one that uses on average a larger product of time and energy, i.e. more action in the same situation as another, will be at a disadvantage. That is why, evolutionary, systems that are organized to achieve lowest average action for all of its agents, will be selected. Therefore self-organization, progressive development and evolution are directed towards minimization of the average action in a system per one event. The system that has the most action efficient configuration is the most organized. This theoretical work is supported by simulations and experimental data and analysis.
The original journal devoted to the science, mathematics and engineering of systems with simple components but complex overall behavior.
Efficiency as generally defined in different fields of complex systems mentioned in the next section.
Academia from different fields of complex system, including physics, mathematics, chemistry, biology, linguistics, computer science, sociology, and economics.
After the conference, full papers of the session are anticipated to be published in the proceedings of Springer Proceedings in Complexity.