  We consider nonequilibrium systems with complex dynamics in stationary states
with large fluctuations of intensive quantities (e.g. the temperature, chemical
potential, or energy dissipation) on long time scales. Depending on the
statistical properties of the fluctuations, we obtain different effective
statistical mechanics descriptions. Tsallis statistics is one, but other
classes of generalized statistics are obtained as well. We show that for small
variance of the fluctuations all these different statistics behave in a
universal way.
