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How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions
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 processe...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group UK
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6052064/ https://www.ncbi.nlm.nih.gov/pubmed/30022170 http://dx.doi.org/10.1038/s41598-018-28962-1 |
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author | Corominas-Murtra, Bernat Hanel, Rudolf Zavojanni, Leonardo Thurner, Stefan |
author_facet | Corominas-Murtra, Bernat Hanel, Rudolf Zavojanni, Leonardo Thurner, Stefan |
author_sort | Corominas-Murtra, Bernat |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-6052064 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | Nature Publishing Group UK |
record_format | MEDLINE/PubMed |
spelling | pubmed-60520642018-07-23 How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions Corominas-Murtra, Bernat Hanel, Rudolf Zavojanni, Leonardo Thurner, Stefan Sci Rep Article 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. Nature Publishing Group UK 2018-07-18 /pmc/articles/PMC6052064/ /pubmed/30022170 http://dx.doi.org/10.1038/s41598-018-28962-1 Text en © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. |
spellingShingle | Article Corominas-Murtra, Bernat Hanel, Rudolf Zavojanni, Leonardo Thurner, Stefan How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title | How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title_full | How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title_fullStr | How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title_full_unstemmed | How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title_short | How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
title_sort | how driving rates determine the statistics of driven non-equilibrium systems with stationary distributions |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6052064/ https://www.ncbi.nlm.nih.gov/pubmed/30022170 http://dx.doi.org/10.1038/s41598-018-28962-1 |
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