Sharp transitions

Yet another issue I had with the concept of entropy is being resolved by this book. I was always curious as to how scientists can say anything concrete about the state of any system, given that it is constantly changing states. If the state of a system is governed by statistical distributions, how can processes occur with distinct boundaries?

For example, we can predict the average kinetic energy of the particles in a litre box at 278K, but at any moment the particles could adopt positions which are unusually close to each other, thus converting some of their kinetic energy to potential energy, and changing the average kinetic energy of the system. But this book explained we can be confident of the exact average energy of the box, because the variance around this mean is so incredibly small, as there are such a large number of particles in the box.

This chapter explains another way we can get sharply defined transitions and values. The concept of co-operativity can explain why some systems can be in discrete distinct states. If the change of state for one molecule can increase the likelihood of another molecule changing state, then a positive feedback loop can occur until all the available molecules switch into the opposite state. The book gives the example DNA stretching and ice melting, but co-operativity comes up everywhere. The reaction of hydrogen gas with oxygen gas to produce water has elements of co-operative behaviour, as the heat produced by the reaction of two molecules can provide the extra necessary heat energy for further molecules to react.

When trying to reconcile this concept with my understanding of entropic processes governed by statistical distributions, I realised that I was still making the assumption that each element in the system is independent of each other. This is clearly not true in these cases when co-operativity is involved. So it seems that in cases where the elements of the system do not behave independently, we can have processes with distinct states that still obey entropic laws.