OK, this post is already way too long, but one final thing. Physicists, I think, become even more drawn to economics when we look into economics and see broad resistance to research pursuing this “complexity” perspective.
It seems instead that most of mainstream research tries to get around system complexity with mathematical tricks, rather than facing up to it. I’m thinking about ideas like representative agents, or rational expectations. The assumptions make it possible to build models without having to deal with the complexity of interactions and the emergent structures they create; but the resulting models, naturally, look very pale and questionable as models of anything real. When physicists see that a small minority of (“heterodox”) economists also find the standard approach hugely limiting, they feel an urge to help out. And they believe that some of their ideas can help.