The release of kinetic energy during explosive volcanic eruptions is a key parameter for hazard assessment and civil defense. The explosive production of volcanic ash by intensive fragmentation of magma and host rocks represents a substantial part of this energy. For cases of explosive eruption where predominantly host rock was fragmented (phreatomagmatic eruptions) to form the major part of volcanic ash, rock mechanical parameters could be measured and fragmentation energies assigned. In cases where most of the produced ash is of juvenile origin (magmatic eruptions) a general method for the determination of fragmentation energy is still lacking. In this article we introduce a thermodynamic approach that relates grain size data of the produced ash deposits to shear rates acting during the deformation of magma. With the use of a standardized fragmentation experiment the physical parameters needed to determine the specific fragmentation energy and deformation history were measured. The experiment was calibrated and tested with two case histories of the Campi Flegrei volcanic field (southern Italy). Both eruptions are classified as "most probable worst-case scenarios" during the next period of activity, to be expected within the next 10--100 years. Using the experimentally determined specific fragmentation energies, the total mass of produced ash of each eruption, and assuming an energy dissipation as observed in the experiments, the total kinetic energy release of the worst-case Campi Flegrei eruptive events to come were calculated with 25 and 40 kt TNT equivalent.