  Nonequilibrium complex systems are often effectively described by the mixture
of different dynamics on different time scales. Superstatistics, which is
"statistics of statistics" with two largely separated time scales, offers a
consistent theoretical framework for such a description. Here, a theory is
developed for log-normal superstatistics based on the fluctuation theorem for
entropy changes as well as the maximum entropy method. This gives novel
physical insight into log-normal statistics, other than the traditional
multiplicative random processes. A comment is made on a possible application of
the theory to the fluctuating energy dissipation rate in turbulence.
