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

Corominas-Murtra, B., Hanel, R., Zavojanni, L., & Thurner, S. (2018). How driving rates determine the statistics of driven non-equilibrium systems with stationary distributions. Scientific Reports 8 (1) e10837. 10.1038/s41598-018-28962-1.

[thumbnail of s41598-018-28962-1.pdf]
s41598-018-28962-1.pdf - Published Version
Available under License Creative Commons Attribution.

Download (1MB) | Preview


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.

Item Type: Article
Uncontrolled Keywords: Statistical physics; Statistics
Research Programs: Advanced Systems Analysis (ASA)
Depositing User: Luke Kirwan
Date Deposited: 20 Jul 2018 11:27
Last Modified: 27 Aug 2021 17:30

Actions (login required)

View Item View Item