Convective Quasi-Equilibrium (CQE) is shown to be a useful framework for understanding the precipitation minus evaporation (P-E) response to CO2-induced warming across a suite of aquaplanet simulations. A linear relationship between the curvature of sub-cloud moist entropy, a marker for the onset of a tropical direct overturning circulation in CQE conditions, and P-E is established through an energy budget analysis of the MPAS model using moist static energy-weighted velocities. The MSE-weighted circulation shows that eddies are the key contributor to the divergence of MSE by the ITCZ over the seasonal cycle. Treating eddies as a diffusive process with constant diffusivity enables P-E to be linked to the curvature of column-integrated MSE, which has a similar seasonal structure to sub-cloud moist entropy. The linear relationship between P-E and the curvature of the sub-cloud moist entropy is shown to exist across many of the simulations from the Tropical Rain belts with an Annual cycle and a Continent Model Intercomparison Project (TRACMIP). This linear relationship is a skillful predictor of changes in P-E in response to CO2-induced warming. The curvature metric also shows improvement in predicting P-E changes compared to the simpler method of relating P-E directly to the sub-cloud moist entropy field.