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Dynamics of complex systems is often hierarchically organized on differenttime scales. To understand the physics of such hierarchy, here Brownian motionof a particle moving through a fluctuating medium with slowly varyingtemperature is studied as an analytically tractable example, and a kinetictheory is formulated for describing the states of the particle. What ispeculiar here is that the (inverse) temperature is treated as a dynamicalvariable. Dynamical hierarchy is introduced in conformity with the adiabaticscheme. Then, a new analytical method is developed to show how theFokker-Planck equation admits as a stationary solution the Maxwelliandistribution modulated by the temperature fluctuations, the distribution ofwhich turns out to be determined by the drift term. A careful comment is alsomade on so-called superstatistics.

Fokker-Planck Theory of Nonequilibrium Systems Governed by Hierarchical Dynamics