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Classification of complex systems by their sample-space scaling exponents
- Source :
- New J. Phys. 20 (2018) 093007
- Publication Year :
- 2018
-
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 thee 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.<br />Comment: 16 pages including supplementary material, revised version
- Subjects :
- Condensed Matter - Statistical Mechanics
Physics - Classical Physics
Subjects
Details
- Database :
- arXiv
- Journal :
- New J. Phys. 20 (2018) 093007
- Publication Type :
- Report
- Accession number :
- edsarx.1806.02386
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1088/1367-2630/aadcbe