Classification of complex systems by their sample-space scaling exponents. (10th September 2018)

• Record Type: Journal Article
• Authors: Korbel, Jan; Hanel, Rudolf; Thurner, Stefan
• Is Part Of: New journal of physics. Volume 20:Number 9(2018:Sep.)
• Publication Date: 2018-09-10
• Subjects: scaling expansion -- extensive entropy -- super-exponential systems -- complex systems -- sample space; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aadcbe
• Languages: English
• ISSNs: 1367-2630

Abstract

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.