20 key concepts in thermodynamics and condensed matter

I gave my last lecture today. This is always a good feeling. Again I went over the 20 key ideas that I hoped they learnt in the course. The most important one, which we have to keep repeating is that in an non-isolated system whose state is defined by pressure and temperature, the Gibbs free energy G can never increase. Consequently, in the equilibrium state G must take the smallest possible value.

On my previous post on the 20 key concepts, Will Polik wrote a helpul comment:

Related to concept 10 (free energy), I think that a key concept in the practical application of thermodynamics is the idea that "the entropy of the universe tends toward a maximum" is equivalent to "the Gibbs free energy of the system (at constant T and P) tends toward a minimum" and the corresponding statement about Helmholtz free energy. This allows one to use just the state properties of the system to determine the direction of change and equilibrium conditions, rather than having to worry about the entire universe!