Monthly Archives: September 2016

”Strong” Ergodicity? A problem of scale and resolution as it’s the norm with everything else

The concept of ergodicity is a scale and resolution dependent concept. Everything can be ergodic if a process or a pattern is analyzed at a scale or resolution that shows ergodic conditions. Yet, there are very few processes or patterns that are truly ergodic and the validity of ergodicity is more related to the question that is posed and how that question is answered. That essentially depends on the fact if people are solving strict mathematical problems / basic science issues or if they are just applying a model which has its own validity on the ergodic assumption.

 

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Information Theory for Complex Systems

All systems in nature can be considered from the perspective that they process information. Information is registered in the state of a system and its elements, implicitly and invisibly. As elements interact, information is transferred. Indeed, bits of information about the state of one element will travel – imperfectly – to the state of the other element, forming its new state. This storage and transfer of information, possibly between levels of a multi level system, is imperfect due to randomness or noise. From this viewpoint, a system can be formalized as a collection of bits that is organized according to its rules of dynamics and its topology of interactions. Mapping out exactly how these bits of information percolate through the system reveals fundamental insights in how the parts orchestrate to produce the properties of the system.

A theory of information processing would be capable of defining a set of universal properties of dynamical multi level complex systems, which describe and compare the dynamics of diverse complex systems ranging from social interaction to brain networks, from financial markets to biomedicine. Each possible combination of rules of dynamics and topology of interactions, with disparate semantics could be translated into the language of information processing which in turn will provide a lingua franca for complex systems.

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