 All right, so we've seen that if we have an isolated system, a system that's thermally isolated from its surroundings, then for that isolated system, a spontaneous process will be one that increases the entropy of the system as a whole, the thing that's isolated from its surroundings. And that's essentially because if the energy is conserved, entropy is the only quantity that matters, and the entropy increasing causes the system to have a higher multiplicity, higher probability, and so moving towards higher multiplicity or higher probability or higher entropy is a spontaneous process. That's fine if we have some process that takes place within an isolated system, but that's not typically the way we set things up in the laboratory. More commonly, for example, if you're doing a reaction in the laboratory, your system might be in solution, but you haven't taken efforts to isolate it from the environment. You haven't wrapped it in a thermally insulating container. So in this case, heat will transfer from the system to the surroundings, to the beaker that it's contained in, or to the air above the solution, or to the broader room or outside the room, the rest of the universe, all of the surroundings of the system. So normally we do things in conditions that are not isolated, but it turns out we can still learn something useful about what the entropy says to us about the spontaneity of a process, even for these non-isolated systems, because we can consider essentially all the rest of the surroundings to be this counterpart of system A. So in this case, we had thermal transfer between part A and part B, just no thermal transfer between those two parts of the system and the rest of the world. In this case, let's consider A to be the system we're interested in, B to be all of the surroundings, and together A and B make up the whole world, the whole universe, everything there is. So in that case, there's thermal transfer between the system and the surroundings, but there's no energy being transferred between the combined system, the entire universe, and anything outside that. So the universe itself is thermally insulated from everything else. So in other words, where in this previous example we had the total entropy being the entropy of system A and the entropy of system B, here we can say the entropy of the entire universe is equal to the entropy of A, or the system, and the entropy of B are the surroundings. So the system and surroundings together combine to make up the entire universe. And the universe, the key observation is the universe itself isn't isolated to the system. It's thermally isolated. So everything that before we could say only about this isolated system, now we can say about the universe as a whole, and in fact that's an important enough statement that we call it the second law of thermodynamics. Then the entropy change for the entire universe for a process is greater than zero. That's analogous to the entropy change for an isolated system being positive. That's going to be a spontaneous process. So if we can get enough information to determine that the entropy of the universe is increasing for a process, we know that process is going to be spontaneous. On the other hand, if the entropy change for the universe is negative, that'll be a non-spontaneous process. It won't happen. That's some process that is not going to happen. That leaves one possibility that we haven't discussed. What if the entropy change is equal to zero? If the entropy change is equal to zero for some process, we say that's an equilibrium process. Essentially, you could say that the process doesn't care whether it does or doesn't happen. If it happens, the entropy change of the universe is negative. If it doesn't happen, or if it happens in reverse, the entropy change of the universe is zero in all cases. So it doesn't matter whether the process happens or doesn't happen. In fact, what happens is the process is constantly happening forwards a little bit, backwards a little bit, none of which is changing the entropy of the system, none of which is changing the probability of either one of those states. So in equilibrium process, it doesn't matter whether state A or state B, the process happens or it doesn't happen. So another word that we've used for an equilibrium process is a process that's reversible. That process happens forwards, backwards, can be reversed quite easily. The opposite of a reversible process is an irreversible process, of course. So a spontaneous process, process that's going to happen spontaneously, like a marker falling due to gravity, or a gas expanding to fill its container, or ice melting at room temperature. Those spontaneous processes happen irreversibly. Because it's spontaneous, the process is going to happen. Once it's midstream happening, it's difficult to turn that process around without a large input of energy. So that's an irreversible process. It doesn't happen smoothly and slowly and reversibly, it happens irreversibly. So that leaves the question, how do we describe what happens for this non-spontaneous process? Would that be a reversible or irreversible? That would be a little bit like asking, if I set this marker on the ground and as I watch it raise itself up against gravity, would that be an irreversible or reversible process? And that's kind of a nonsense question. If a process is non-spontaneous because it's not going to happen at all, then because it doesn't happen, it doesn't make sense to ask whether it happens reversibly or happens irreversibly. Irreversibly means it is spontaneous enough. It's going to happen and it will happen irreversibly. If the entropy changes zero and the process is in equilibrium, that can happen reversibly. When it doesn't happen, when it's not spontaneous, it's pointless to ask whether when it happens, it would be irreversible or reversible because it's not going to happen at all. So in general, however, this third column is just an extra set of terminology that we can use to describe these processes. The second law of thermodynamics tells us, if we know the sign of the entropy change for the universe as a whole, then we can predict whether a process is going to happen spontaneously. Whether it won't happen, it's non-spontaneous or whether that process is in equilibrium.