Timeline for Value of $\Omega(0)$?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 5, 2021 at 20:16 | vote | accept | michael b | ||
| Jun 5, 2021 at 20:16 | answer | added | SolubleFish | timeline score: 2 | |
| Jun 5, 2021 at 20:15 | comment | added | michael b | Nevermind, I understand this now. In canonical ensembles ($NVT$), the temperature, and therefore $\beta$, is an external (independent) parameter, hence (2) is valid in that context. In the $NVE$ ensemble it isn't. That's a good enough answer for me. | |
| Jun 5, 2021 at 20:13 | comment | added | michael b | Is $\beta$ not an external parameter in the microcanonical ensemble? And yes, I do see that applying the Laplace transform inherently changes it to the canonical ensemble. But I would've thought that the definition in (3) holds in either case. Maybe this calculation is evidence that it does not. | |
| Jun 5, 2021 at 19:59 | comment | added | SolubleFish | Ok, but when you are computing the Laplace transform, you are switching to the canonical ensemble, where $\beta$ is a external parameter. You cannot use $(3)$ in the integral defining $Z(\beta)$ | |
| Jun 5, 2021 at 19:28 | comment | added | michael b | It's the definition of $\beta$ in the microcanonical ensemble, and by extension, in general. Alternatively written as, $\beta = \partial \ln \Omega / \partial E$. And yes, that's true, but by that argument so is the average energy, yet we can write an equation for it that makes it dependent on other quantities, such as $P_r$. | |
| Jun 5, 2021 at 18:26 | comment | added | SolubleFish | Where does $(3)$ come from ? In the Legendre transform $\beta$ is an independent variable. | |
| Jun 5, 2021 at 15:35 | history | asked | michael b | CC BY-SA 4.0 |