This paper investigates the landscape of extremum characteristics for different energy consumption terms in gas-solid fluidization based on the Energy Minimization Multi-Scale (EMMS) model. The influence of typical cluster correlations on the extremum characteristics is also investigated to consolidate the results. The energy consumption terms are resolved into three types, i.e. suspension ("s"), transport ("t") of the particles and pure dissipation ("d") caused by their collisions and acceleration. Three regimes which are particle-dominated (PD), fluid-dominated (FD), and particle-fluid compromising (PFC) respectively subject to the extrema of epsilon = min, W-st = min and N-st = min, are investigated. Then the same procedure is extended to individual and combined terms (i.e. "s", "t", "d", "s+t", "t+d", "d+s") of energy consumption with respect to unit mass of particles ("N") and to unit volume of bed ("W"). The study of extremum characteristics reveals an enclosure structure which features an upper voidage regime corresponding to minimum energy dissipation rate (MinED), a lower voidage regime to maximum energy dissipation rate (MaxED) and a so-called mesoregime in between. The landscape of extremum characteristics reveals that the stability condition must be constructed according to clear physical meaning, otherwise misleading may occur due to multiple contradictive extrema exist in specific regimes. Although the clustering effects on extremum characteristics exposed some limitations of current correlations, the above-mentioned characteristics are found to be insensitive to cluster diameter correlations, indicating that the findings are intrinsic to the EMMS model. Further work is still needed to explore the mesoscale structure and its relationship with extremum behavior as well as underlying physics in fluidization.