I am talking about higher probability viz. Brownian Motion, Ergodic Theory, Concentration, Percolation, Random Graphs, Random Matrix, etc. Going through books, I find that somehow or the other, many theorems in probability come from motivation from physics: they observe a physics phenomenon, then they think about it mathematically, and out comes a theorem.
Probably I'll give an example. Dynamical systems are, in my opinion, an offshoot of physics. The very concept of ergodicity i.e. measure-theoretic non-decomposability of the system into two non-trivial components can be best motivated using the free flow of gas molecules in a room, rather than just writing some dry $T^{-1}A=A\implies \mu(A)\mu(A^c)=0$.
The latter is of course fine, and rigorous and precise, but does not really tell the story.
I want to do research in probability. I have a firm understanding of the mathematics. However, I have not done any undergraduate or graduate physics course. So I am afraid that despite knowing the maths, my knowledge will be dry and if I wish to devise a theorem, I have to heavily rely on measures and stuff, on purely mathematical inequalities, although if I have an understanding of statistical mechanics, then at least I would be able to "guess" what my bounds can be, say for inequalities, or what I really want to say.
Your opinion is highly solicited. To be a good researcher in probability, would it be better for me to learn physics? If so, which part? Any book recommendation? Particularly any book that "connects" probability with physics?
Thanks a lot!