Timeline for Two definitions of the density matrix?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 29, 2016 at 3:07 | vote | accept | biryani | ||
| Apr 28, 2016 at 18:52 | comment | added | udrv | Technically, since $\rho_eq$ commutes with the Hamiltonian $H$, it is a time-independent solution of the Liouville-von Neumann eq. in the absence of interactions, that is, ${\dot \rho_eq} = 0$. Thermal equilibrium with the surroundings corresponds to the limit of vanishing interactions with the surroundings, so yes, you are correct. But it applies to an isolated system too. | |
| Apr 28, 2016 at 9:32 | answer | added | Mark Mitchison | timeline score: 7 | |
| Apr 28, 2016 at 6:34 | comment | added | biryani | Thanks. If I understand you correctly then the second definition defines the state of the system that is in equilibrium with its surrounding. (Which I assume is at a temperature $1/k \beta$). | |
| Apr 28, 2016 at 6:28 | comment | added | udrv | Actually there is only the first definition. The 2nd one defines the thermal equilibrium state $\rho_{eq} = e^{-\beta H}/Z$ for inverse temperature $\beta = 1/kT$ and is a particular case of the first. So no, the 2nd one is not independent of the state, it is the state. If the system's density matrix is some $\rho \neq \rho_{eq}$ then the system is away from equilibrium. | |
| Apr 28, 2016 at 6:19 | history | asked | biryani | CC BY-SA 3.0 |