# Mathematical transformations and physics

1. Jan 10, 2012

### nonequilibrium

In relation to thermodynamics or statistical mechanics, it is often briefly mentioned that the partition function is the Laplace transform of the microcanonical $\Omega$, or that the Helmholtz free energy is the Legendre transformation of entropy, etc. But in the courses I've had, it stayed to simply noting these facts.

I was just wondering, is there a deeper reason for these appearances of transformations in these contexts? More specifically: is there a more mathematical book on statistical mechanics that actually gives these matters sufficient attention (and their reason should then be that it leads to elegant physics, not just for the math of it, if you understand what I mean).