Classification of complex systems by their sample-space scaling exponents

Korbel, J., Hanel, R., & Thurner, S. (2018). Classification of complex systems by their sample-space scaling exponents. New Journal of Physics 20 (9) e093007. 10.1088/1367-2630/aadcbe.

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Abstract

The nature of statistics, statistical mechanics and consequently the thermodynamics of stochastic systems is largely determined by how the number of states W(N) depends on the size N of the system. Here we propose a scaling expansion of the phasespace volume W(N) of a stochastic system. The corresponding expansion coefficients (exponents) define the universality class the system belongs to. Systems within the same universality class share the same statistics and thermodynamics. For sub-exponentially growing systems such expansions have been shown to exist. By using the scaling expansion this classification can be extended to all stochastic systems, including correlated, constraint and super-exponential systems. The extensive entropy of these systems can be easily expressed in terms of these scaling exponents. Systems with super-exponential phasespace growth contain important systems, such as magnetic coins that combine combinatorial and structural statistics. We discuss other applications in the statistics of networks, aging, and cascading random walks.

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