Timeline for Setting of the canonical ensemble for actual interacting systems
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 15, 2023 at 0:28 | comment | added | Wade Hodson | If there are a large # of spins, then the argument in @RogerVadim's answer will at least establish that any subset of spins which is itself large (yet small relative to the total # of spins) can be described by a canonical ensemble (assuming again that the whole system is described w/ a MC ensemble). As for the question of ergodicity of such a system, I definitely don't know enough to say. It's at least conceivable that while the mechanical d.o.f. could be harmonic and therefore nonergodic in isolation, the spins + mechanical d.o.f. might still be approximately ergodic when coupled together. | |
| Feb 14, 2023 at 17:35 | vote | accept | Erithacus Rubecula | ||
| Feb 14, 2023 at 17:35 | comment | added | Erithacus Rubecula | These conditions seem rather restrictive. If we imagine our Ising spins living on the atoms of a crystal lattice, with interaction strength J depending on the distance between adjacent atoms (to have coupling), the heat bath of the canonical Ising model is naturally interpreted, I suppose, as the mechanical degrees of freedom of the lattice (and the mechanical energy thereof as "heat"), which are not that many wrt the number of spins, and not necessarily ergodic, if the crystal is harmonic for instance. | |
| Feb 13, 2023 at 19:11 | history | edited | Wade Hodson | CC BY-SA 4.0 |
I edited the paragraphs on the justification of the microcanonical ensemble, to include the fact that chaotic dynamics (in addition to ergodicity) are also necessary to fully justify the microcanonical description.
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| Feb 13, 2023 at 18:42 | history | answered | Wade Hodson | CC BY-SA 4.0 |