We describe a thermodynamic-motivated, information theoretic analysis of proteomic data collected from a series of 8 glioblastoma multiforme (GBM) tumors. GBMs are considered here as prototypes of heterogeneous cancers. That heterogeneity is viewed here as manifesting in different unbalanced biological processes that are associated with thermodynamic-like constraints. The analysis yields a molecular description of a stable steady state that is common across all tumors. It also resolves molecular descriptions of unbalanced processes that are shared by several tumors, such as hyperactivated phosphoprotein signaling networks. Further, it resolves unbalanced processes that provide unique classifiers of tumor subgroups. The results of the theoretical interpretation are compared against those of statistical multivariate methods and are shown to provide a superior level of resolution for identifying unbalanced processes in GBM tumors. The identification of specific constraints for each GBM tumor suggests tumor-specific combination therapies that may reverse this imbalance.