Observables in Statistical Physics¶

Observables in Equilibrium State¶

In statistics, the average of an observable is

where \(\rho\) is the “probability matrix”. In QM, this is

If a system of QM comes to equilibrium, that means

1. \(\rho = \frac{ e^{-\beta H} }{\mathrm{Tr} e^{-\beta H} }\);
2. \(\rho\) is diagonal in energy eigen space.