The recently developed Hartree analysis for compressible diblock copolymers has been performed to study the thermodynamic origin of an immiscibility loop and its unprecedented pressure dependence observed in a diblock copolyrner from polystyrene and poly(n-pentyl methacrylate). Certain specific interactions (SI) were incorporated in the theory by adding an entropic component into cross-contact interactions. An effective Flory-type interaction parameter y(cRPA), which carries not only the change in contact interactions but also compressibility difference between blocks, was shown to play a central role here. The %eRPA plotted against temperature exhibited a loop character with a maximum because of the input SI. The effects of both fluctuations and compressibility difference were found through XcRPA to yield a loop phase diagram for the copolymer in a feasible temperature range along with the peculiar dependence of the loop on copolymer chain sizes and pressure. The resultant theoretical phase behavior was shown to be harmonious with the experimental observations for the copolymer.