A full understanding of the jamming transition remains elusive, but recent advances which draw upon the common features of frustrated systems are encouraging. Herein, we show that, for mixtures of oil and silica particles, the dependence of the dejamming stress on filler volume fraction, phi is consistent with the shape of a reported jamming phase diagram [Trappe, Nature (London) 411, 772 (2001)]. We discover for the first time, however, that the role of phi disappears when mechanical energy input, defined as stress multiplied by strain, is used instead of stress as the critical parameter. We also examine literature results for aqueous suspensions of boehmite alumina powders, latex dispersions of polystyrene particles, and carbon black-filled elastomers in order to illustrate the universality of our finding. This study provides evidence for a thermodynamic interpretation of the jamming transition.