Before revision:  We have examined 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 as well as to first and the second order phase transitions between them.
After revision:  We have examined 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.