One of the current problems in the study of complex systems in general and Complex Adaptive Systems in particular, is how we measure them, and since the measurement of these systems is a basic requirement to a time to compare systems in a scientific and seek their optimization.
This is an open question, but there are alternatives that have been proposed, the latter of which I read in the book " Cosmic Evolution: The Rise of Complexity in Nature. Eric J. Chaisson."
presenting the complex history of the author tries to prove 2 things. On the one hand claims to show that increases in complexity are compatible with the second law of thermodynamics . The second law, in its statistical mechanical interpretation requires that the disorder increases in a closed system implying that the complexity (as opposed to deodorant) should decrease. However, a complex structure like a galaxy, a star or an organism is an open system, capable of sustaining sufficient complexity to exporting disorder to their environment, to more than justify their internal complexity increases. In fact, the second law is maintained because the disorder if increases in the larger system, one consisting of the complex structure but the surrounding environment. For example, increasing complexity in a young star, has a balance disorder that exports to its environment through radiation.
Your second goal is to demonstrate that the physical phenomenon that occurs complexity is the same for all these transitions . Very basic form that explains the phenomenon is as follows: Where there are strong gradients of energy, sometimes the conditions are correct for the spontaneous emergence of structures that tend to dissipate these gradients. While this gradient exists, these structures posrán be stable, maintained in a quasi-stable state of high complexity, this is far from equilibrium statistical-mechanical sense, by the flow of energy through them.
A classic example is the hurricane . This is a structure that arises from a thermal gradient enters the upper and lower atmosphere. This structure is complex, dissipative, ie allowing the reduction of this gradient by transferring warm air from the sea surface to the cold upper atmosphere.
The author argues that the stars are also dissipative structures dsipando energy gradients produced by the collapsing hydrogen clouds by gravitational force, or that biological organisms also confirm dissipative structures of the species contained high energy gradient between complex chemical structures of their food source, and low complexity of their excrement.
But how we measure complexity? This author proposes that a measure of its complexity can be the energy density. or the rate of flow of energy through dek system per unit mass, or φm. This amount, he argues, would be inversely proportional to the disorder of the system, and therefore in direct correlation with its complexity.
This assertion is not free of problems, however φm has the great virtue of being measurable in real systems. In this book the author shows the measurement calculations for a wide range of systems, including the sun (φm ~ 2 ergs / sec / gram), the human mind (150.000 ergs / sec / gram) and human civilization (500.000 ergs / sec / gram). Also a very interesting series of diagrams, he shows that galaxy φm society increases, and therefore also increases over time.
Because then this trend would exist φm? Basically, the author explains that in systems far from equilibrium (including the universe) the dominant dissipative structures are those that are able to capture the largest proportion of energy flow. Φm therefore should increase as new structures emerge (for fluctuations or mutations) and as the system "discovers" new routes dissipative.
This is an interesting alternative in learning about complex systems, its modeling and quantification.
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