My textbook gives this example of a reversible process: A gas in a piston is expanded over a long period of time, sitting on a hot plate that maintains its temperature. As an infinitesimal amount of weight is released (allowing it to expand), it is in thermal equilibrium. This process is reversible because at every point in time the object is in thermal equilibrium with the reservoir.
Then the book says that the reverse of this process is not reversible. They suggested that reversing this process would bring the entropy back to its original value from a higher one, contradicting the increase of entropy postulate. They say, "That postulate holds only for irreversible processes in closed systems. This process is not irreversible, and the system is not closed." Why is this system not closed, but the original one was? Will the entropy decrease back to its original value?