Sumiyoshi Abe, Christian Beck, Ezechiel G. D. Cohen
Complex systems are frequently governed by a hierarchy of dynamics on different time scales. Superstatistics, which is a "statistics of statistics" with several largely separated time scales, aims to describe their nonequilibrium stationary states. Here, a prototype system, i.e., a Brownian particle moving through a fluctuating medium with slowly varying temperature, is considered, and a Fokker-Planck theory is developed to establish a dynamical foundation of superstatistics, which includes time evolution. In this theory, both the velocity of the particle and the inverse temperature are dynamically treated with the help of a Born-Oppenheimer-like adiabatic scheme introducing a dynamical hierarchy. It is shown that the Fokker-Planck equation admits then as a general stationary solution a superstatistical one. Three major universality classes often observed in nature, i.e., gamma, inverse gamma, and log-normal superstatistics, are discussed as special solutions.
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http://arxiv.org/abs/1208.1957
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