 So I'm going to try to go after and understand the property if I have a long chain that could either be random or if I take this chain and have some segments of the chain that are turning up into alpha helix. This is a famous example and we're talking about helix-coil mixing or helix-coil equilibrium and the book goes into a lot of detail there. In principle this is some sort of transition. We don't know what type of transition is this yet and I'm interested in how much can these coexist? Do they mix and what are the average length of these segments going to be? That relates intimately to other mixtures. You can imagine having say let's say we have a large lake or system of water and then we have a piece of ice in the system so that water and then ice but here is where things start to deviate a bit. So in general for a three-dimensional system you will always have separation of phases. Remember that hydrophobic effect. The reason why we get the separation of phases is Leve Landau is the one who has derived this. It's not that hard at least if we hand wave about it. This is going to depend on the surface here right? In general there is some sort of surface energy here and the surface energy is first going to depend on some sort of energy that is depends on the interaction and then the number of atoms or molecules that I put on that surface. If that energy is negative it would always be good and then things would mix perfectly so that's not the case here. We do know that they want to separate. The question then is how expensive is it? Well the expense there is going to be proportional to the surface. On the other hand the number of residues I have in a particular phase here is proportional to the volume. So here I would argue that the delta G surf the surface energy is roughly proportional to the number of residues raised to the power of two-third. It's exactly the same argument as hydrophobic effect and what this means is that the larger the system is this is going to go up fairly quickly. So even if n raised to the powers of two-thirds is not that gigantic it's certainly something that goes much faster than the logarithm of n and the remaining components here which the book goes into some detail is you can place these eyes in many different places right but that's always going to be entropy related and that means that there are logarithms of n showing up there. So because of this surface tension here and the dimensionality whether it's two or three dimensions doesn't matter where it's always going to be expensive to mix faces. Now you might say that if it's bring or fall you occasionally see a sheet of ice floating in water that's true but it's never going to be stable there. So if you froze the temperature at that specific moment eventually everything will turn into either pure ice or pure water. So what we're seeing there is just an effect of the kinetics it will not happen instantly but that's in three dimensions. In two dimensions the world's or even one dimension the world behaves very differently. How large is the interaction surface here? So I have one point there one point there one point there one point there one point there and one point there and this is really constant or at least just proportion to the number of helical elements I have here. So there is no obvious factor here that will mean that it's better to separate them than having a large piece of helix. So there won't really be an effect here that is proportional to a surface. So one in a system that is one-dimensional faces can coexist it's a very deep result in physics that Lev Landau has proposed. My point here is not going to be to rehash all of Lev Landau's writing and awesome as it is but the point is that for a helix coil transition we will not have a proper phase transition. The phases can coexist and we will see some mixing and we're going to try to calculate a little bit and use that to derive some delta g values.