How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2018-12

AUTHORS

Bernat Corominas-Murtra, Rudolf Hanel, Leonardo Zavojanni, Stefan Thurner

ABSTRACT

Sample space reducing (SSR) processes offer a simple analytical way to understand the origin and ubiquity of power-laws in many path-dependent complex systems. SRR processes show a wide range of applications that range from fragmentation processes, language formation to search and cascading processes. Here we argue that they also offer a natural framework to understand stationary distributions of generic driven non-equilibrium systems that are composed of a driving- and a relaxing process. We show that the statistics of driven non-equilibrium systems can be derived from the understanding of the nature of the underlying driving process. For constant driving rates exact power-laws emerge with exponents that are related to the driving rate. If driving rates become state-dependent, or if they vary across the life-span of the process, the functional form of the state-dependence determines the statistics. Constant driving rates lead to exact power-laws, a linear state-dependence function yields exponential or Gamma distributions, a quadratic function produces the normal distribution. Logarithmic and power-law state dependence leads to log-normal and stretched exponential distribution functions, respectively. Also Weibull, Gompertz and Tsallis-Pareto distributions arise naturally from simple state-dependent driving rates. We discuss a simple physical example of consecutive elastic collisions that exactly represents a SSR process. More... »

PAGES

10837

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1038/s41598-018-28962-1

DOI

http://dx.doi.org/10.1038/s41598-018-28962-1

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1105573323

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/30022170


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139 https://www.grid.ac/institutes/grid.75276.31 schema:alternateName International Institute for Applied Systems Analysis
140 schema:name Complexity Science Hub Vienna, Josefstädterstrasse 39, 1080, Vienna, Austria
141 IIASA, Schlossplatz 1, 2361, Laxenburg, Austria
142 Santa Fe Institute, 1399 Hyde Park Road, 87501, Santa Fe, NM, USA
143 Section for the Science of Complex Systems, CeMSIIS, Medical University of Vienna, Spitalgasse 23, A-1090, Vienna, Austria
144 rdf:type schema:Organization
 




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