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Sample space reducing (SSR) processes offer a simple analytical way tounderstand of the origin and ubiquity of power-laws in many path-dependentcomplex systems. SRR processes show a wide range of applications that rangefrom fragmentation processes, language formation to cascading pro- cesses. Herewe argue that they also offer a natural framework to understand stationarydistributions of generic driven non-equilibrium systems that are composed of adriving and a relaxing process. We show that the statistics of drivennon-equilibrium systems can be derived from the understanding of the nature ofthe underlying driving process. For constant driving rates exact power-lawsemerge with exponents that are related to the driving rate. If driving ratesbecome state-dependent, or if they vary across the life-span of the process,the functional form of the state-dependence determines the statistics. Constantdriving rates lead to exact power-laws, a linear state-dependence functionyields exponential or Gamma distributions, a quadratic function gives thenormal distribution. Logarithmic and power-law state dependence leads tolog-normal and stretched exponential distribution functions, respectively. AlsoWeibull, Gompertz and Tsallis-Pareto distributions arise naturally from simplestate-dependent driving rates. We discuss a simple physical example ofconsecutive elastic collisions that exactly represents a SSR process.

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