We have located links that may give you full text access.
How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions.
Scientific Reports 2018 July 19
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.
Full text links
Related Resources
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app
All material on this website is protected by copyright, Copyright © 1994-2024 by WebMD LLC.
This website also contains material copyrighted by 3rd parties.
By using this service, you agree to our terms of use and privacy policy.
Your Privacy Choices
You can now claim free CME credits for this literature searchClaim now
Get seemless 1-tap access through your institution/university
For the best experience, use the Read mobile app