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

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http://eprints.org/relation/isVersionOf https://pure.iiasa.ac.at/id/document/84713 http://eprints.org/relation/isVolatileVersionOf https://pure.iiasa.ac.at/id/document/84713 http://eprints.org/relation/issmallThumbnailVersionOf https://pure.iiasa.ac.at/id/document/84713 archive 353 disk0/00/01/53/77 2018-07-20 11:27:22 2021-08-27 17:30:34 2018-07-20 11:27:22 article show Corominas-Murtra B. Hanel R. Zavojanni L. Thurner S. 1918 How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions pub prog_asa Statistical physics; Statistics 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. 2018-07-18 published NPG 10.1038/s41598-018-28962-1 307 public Scientific Reports 8 1 e10837 TRUE 2045-2322 FALSE no info:eu-repo/semantics/article