Supported nano-metal catalysts are widely used in industrial processes. There is a trade-off between the activity and stability from mesoscale, which can be effectively tackled with the principle of compromise in competition (mechanisms A and B). To apply mesoscience methodology in this specific area, this work summarized research progress, where direct H₂O₂ synthesis was chosen as a typical case to identify and represent mechanism A (activity) and mechanism B (stability). It was found that mechanism A has been widely studied, while mechanism B still cannot reflect explosion. Subsequently, reaction heat and fusion enthalpy were proposed to represent mechanism B in this work, and the molecular thermodynamic model was identified as an effective tool for the study. A corresponding framework for mechanism B was constructed and the progress in developing the model for this particular purpose was provided. Finally, perspectives were discussed based on the linear non-equilibrium thermodynamics.