Quantum mechanics + statistical physics = ?

Quantum mechanics and statistical physics use very similar and inter-connected concepts. E.g., the latter is concerned with distribution and probabilities, while the former operates with wave functions and amplitudes. Even the essential equations, master and Shrodinger, appear to be similar:

\begin{equation} \frac{\mathrm{d}}{\mathrm{d} t} \psi(t) = H \psi(t) \quad\text{and} \quad i \frac{\mathrm{d}}{\mathrm{d} t} \psi(t) = H\psi(t) . \end{equation}

The only difference is the imaginary factor i! But these similarities lie just on the surface...

You can read more about it in a draft paper by J. C. Baez and J. Biamonte [1]. Please be sure to buy one, if you like and if it becomes available! Currently you can get from the arXiv website (see the references section).