Superstatistics as the statistics of quasiequilibrium states: application to fully developed turbulence.

In nonequilibrium states, currents are produced by irreversible processes that take a system toward the equilibrium state, where the current vanishes. We demonstrate, in a general setting, that superstatistics arises when the system relaxes to a (stationary) quasiequilibrium state instead, where only the mean current vanishes because of fluctuations. In particular, we show that a current with gaussian white noise takes the system to a unique class of quasiequilibrium states, where the superstatistics coincides with Tsallis escort q distributions. Considering the fully developed turbulence as an example of such quasiequilibrium states, we analytically deduce the power-law spectrum of the velocity structure functions, yielding a correction to the log-normal model, which removes its shortcomings with regard to the decreasing higher order moments and the Novikov inequality, and obtain exponents that agree well with the experimental data.