# If entropy is a state function, then why is all the talk about reversible vs. irreversible processes?

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.

• Here is what solved the same confusion to me when I was at your point: "A state function is NOT the same thing as a mechanical potential.". It does look pretty much like one, does it not, with the definition of different paths that the system can take and all? So what's the difference? The difference is that in potential problems the potential is the only relevant physical quantity. It completely determines the dynamics of the system. In thermodynamics that's not the case. The relevant physics in thermodynamics is the heat transfer between temperature baths, which is an irreversible process. – CuriousOne Jun 6 '15 at 20:35
• Hmm, thanks for the comment. I'm not sure I entirely get this, but you are totally right that in my head I treated these two, namely state functions and mathematical potentials as the same. I'm quite surprised they are not the same, actually. I will try and understand what you are saying here. – Benjamin Márkus Jun 7 '15 at 15:41

1. In case of $S(A)=S(B)$ there are many paths to connect $A$ to $B$ but only a single one that is reversible, i.e. can be traveled both ways without increasing the total entropy in the universe. This result is very important in cyclic processes.