How is one process reversible and its reverse non-reversible? 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? 
 A: If a process is reversible, then the same process run backwards in time is also reversible. 
The system you describe is not closed because heat enters through the hot plate. This is true no matter the direction of the process. When the piston expands, heat enters the piston and the piston does work on the weight holding down the piston. The entropy change of the piston is positive, and can be calculated by $\int \mathrm{d}Q/T$
When the piston contracts, the weight on the piston does work on it and the piston gives off heat. It gives off exactly the same amount of heat as before and loses the same amount of entropy as it gained in the expansion process.
The entropy that the piston gains / loses is equal to the entropy that the surrounding system loses / gains, so the entropy of the universe is constant in both cases.
I don't know why your textbook says that one process is reversible and the same process backwards is not. Maybe try reading that part very carefully and make sure you're interpreting it correctly. Could it be talking about contracting the piston with a single heavy weight instead of an infinite series of infinitesimal weights, for example?
