Are all Quasi-static Processes Reversible?

A process, carried out in a stepwise manner, becomes quasi-static when the number of intermediate steps tends to infinity. Usually, the net entropy production approaches zero under this limiting condition. Hence, such cases are termed reversible. A favorite example is the introduction of an infinite number of intermediate-temperature reservoirs in between the source and the sink for a non-isothermal heat transfer process. We analyze the situation and conclude that such quasi-static processes are not reversible. Indeed, no non-isothermal heat transfer process can ever be made reversible due to an extraneous work term.