Before revision:  We examine the main thermodynamic consequences of the existence of this type of multifractality related to the thermal stable, metastable, and unstable phases within a hierarchy of fluctuations, and also to the first and second order phase transitions between them  .
After revision:  We examine the main thermodynamic consequences of the existence of this type of multifractality related to the thermal stable, metastable, and unstable phases within a hierarchy of fluctuations, and also to the first and second order phase transitions between them as well. These phase transitions are of the first and second orders according to the modified Ehrenfest classification, sometimes called the Mandelbrot one .