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

Scientific Reports
Bernat Corominas-MurtraStefan 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 an...Continue Reading

References

Jul 27, 1987·Physical Review Letters·P BakK Wiesenfeld
Oct 16, 1999·Science·A L Barabasi, R Albert
Apr 15, 2015·Proceedings of the National Academy of Sciences of the United States of America·Bernat Corominas-MurtraStefan Thurner
Jun 13, 2015·Journal of the Royal Society, Interface·Stefan ThurnerBernat Corominas-Murtra
Apr 19, 2017·Physical Review. E·Tamás S Biró, Zoltán Néda
Sep 13, 2017·Scientific Reports·Bernat Corominas-MurtraStefan Thurner

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Citations

Nov 1, 2018·Entropy·Rudolf Hanel, Stefan Thurner

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