So I'm preparing for my Thermodynamics undergrad exam, and I just can't wrap my head around the significance of reversibility vs. irreversibility of a process in relation to entropy. I mean if entropy is a state function, and a system in state A has S(A) entropy, and a system in state B has S(B), then what do we care whether the path between them is reversible or irreversible?
Also, my professor has stated that in an irreversible cycle the change in entropy is not zero. How can that be if a cycle is defined by having the exact same state as start and end, and entropy is a state function?
All this confuses me a lot, and I'd really appreciate some clarification.