A process is reversible if and only if it's always at equilibrium during the process. Why?
I have heard several specific example of this, such as adding weight gradually to a piston to compress the air inside reversibly, by why should it be true in general?
EDIT: Here is something that would firmly convince me of this: Suppose I have a reversible process that is not always in equilibrium. Describe a mechanism for exploiting this process to create a perpetual motion machine.