Physical meaning of temperature in superstatistics

Abstract

We show that the fluctuating temperature in the superstatistics construction is proportional to the average (arithmetic mean) energy per degree of freedom of the system in the thermodynamic limit. The latter is a fluctuating quantity due to the strong correlation of statistical nature introduced by superstatistics between degrees of freedom. The necessity for scale dependence of the parameters of superstatistics, which can be explicitly realized through applications of superstatistics in isotropic turbulence, is discussed.