Letting pi : X -> Y be a one-block factor map and Phi be an almost-additive potential function on X, we prove that if pi has diamond, then the pressure P(X, Phi) is strictly larger than P(Y, pi Phi). Furthermore, if we define the ratio rho(Phi) = P(X, Phi)/P(Y,7 pi Phi), then rho(Phi) > 1 and it can be proved that there exists a family of pairs {(pi(i), X(i))}(i=1)(k) such that pi(i) : X(i) -> Y is a factor map between X(i) and Y, X(i) subset of X is a subshift of finite type such that rho(pi(i), Phi vertical bar x(i)) (the ratio of the pressure function for P(X(i), Phi vertical bar x(i)) and P(Y, pi Phi)) is dense in [1, rho(Phi)]. This extends the result of Quas and Trow for the entropy case.
