Why do we always see the claim that an isentropic process for a system is adiabatic and reversible? The change in entropy for a process is the sum of the entropy transfer accompanying heat and the entropy production. The entropy production term is always at least zero, and the transfer term follows the direction of heat flow. Thus it seems reasonable that we could have an irreversible process where heat is transferred from the system (an entropy decrease for the system) in the right proportion to match entropy produced within the system. Thus the two processes would cancel and the entire process would be isentropic and yet not adiabatic.