Before revision:  We examine the main thermodynamic consequences of the existence of this type of multifractality . They can be expressed directly in the language of  thermally stable, metastable, and unstable phases , and phase transitions between them as well .
After revision:  We examine the main thermodynamic consequences of the multi-branched multifractality are revealed. These are directly expressed in the language of thermally stable, metastable, and unstable phases , and phase transitions between them as well .