  We report an evidence that self-similar and anomalous scalings coexist in a
turbulent medium, particularly in fluctuations of the magnetic field flux
density in magnetized plasma of the solar photosphere. The structure function
scaling exponents in the inertial range have been analyzed for fluctuations
grouped according to the sign of the path-dependent stochastic entropy
production. It is found that the scaling exponents for fluctuations with the
positive entropy production follow the phenological linear dependence for the
magnetohydrodynamic turbulence. For fluctuations with the negative entropy
production, the scaling is anomalous.
