 What I love with this way of describing the world is that it can tell us a lot about systems without us having to assume anything about them. So let's then look at how this entropy varies as a function of energy. On one axis here we have entropy, S, and on the other one we have energy, E. And what happens is I'm pumping more energy into the system. Typically we're going to have a curve that looks something like that. At any particular point here there's going to be a derivative and that derivative is 1 over t. What that means in practice is that as I'm pumping in more energy the system can decide where it wants to be here. The reason why it stays on this line is that with a little bit of exercise you can probably know that in this half the free energy is going to be smaller than the zero value here. And in this area the free energy is going to be higher than free energy zero. So it's good to be here but you can't get further up here because that would require me to move to a different type system. I will in the next course I'm going to be looking at what happens when I move along this line. But before we do that let's just hypothetically consider other possibilities. What if I had a line that looked maybe that way or that way? Well in both these cases the temperature would be smaller than zero. Can that happen? Yes it can but not the way you think because there's an important qualifier here. It can happen but it can't happen at the equilibrium. We will not have equilibrium in those points but the world would be pretty boring if we only had equilibrium because in particular in life science at equilibrium we're all dead. The type of processes this corresponds to is very rapid non-equilibrium processes such as gas flowing out through a valve. At the very point where the gas is leaving the valve pressure isn't really defined it's just expanding. And at that point we don't have equilibrium and then you can have processes like this. We can also have a type of curve that would look that way. Here I have a well defined temperature that's finite. But look at the free energies there. This means that we're at the worst possible free energy value I could imagine. Moving along this curve would put me in a better position whereas moving along this curve would put me in a worse position. But this can happen. This corresponds to a local maximum. Remember those energy landscapes we talked about. So standing in this point is balancing on the edge of a knife the peaks in the energy landscapes which is going to be important for kinetics later. If anybody perturbs me epsilon in one direction here I'm going to fall down either on the left or the right because then I'm no longer at the maximum derivative here and then I will have a more normal process but as long as I'm just standing there and not moving I can balance.