Physics
Physics is very well defined as a theory, so it translates well to programming simulations and subsequently, game design. However, physics is a separate field from PCG. Still, physics can be used to aid us in our execution of PCG.
An example of using physics as a mechanism of PCG is the popular mobile game, Angry Birds. In Angry Birds, a modular structure is presented but it then has physics applied to it as a means to restructure it. The effects of the physics create new structures that then impact how the game is played.
The trade-off is that physics requires a lot of processing power. Current technology now provides dedicated hardware to processing just the physical simulations in games. It can add very unique game playthrough.
Physics is its own field of study, so it is a good place to start when researching new ways to apply physics to PCG. There are a lot of physics engines available such as the Open Dynamic Engine, so it might be more...