Timeline for Why is there no Gibbs correction or Fermi statistic when calclulating the entropy of $N$ harmonic oscillators?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| Apr 28 at 0:14 | comment | added | mike stone | The oscillators are distinguishable. | |
| Jun 18, 2020 at 13:36 | comment | added | user224659 | Abstract: Boltzmann Correction Factor (BCF) N! is used in micro canonical ensemble and canonical ensemble as a dividing term to avoid Gibbs paradox while finding the number of states and partition function for ideal gas. For harmonic oscillators this factor does not come since they are considered to be distinguishable. We here show that BCF comes twice for harmonic oscillators in grand canonical ensemble for entropy to be extensive in classical statistics. Then we extent this observation for all distinguishable systems. | |
| Jun 18, 2020 at 13:35 | comment | added | user224659 | I think ths paper answers my questions lajpe.org/dec14/4302_Udayanandan.pdf thanks though! | |
| Jun 18, 2020 at 13:33 | comment | added | user245141 | how do you use the Gibbs factor in an ideal gas? | |
| Jun 18, 2020 at 13:21 | comment | added | user224659 | I really don't get your first point @yu-v. Isn't this what I'm doing? I assume the energy spectrum $H=\sum_i(n_i+1/2)\omega$ and then take the partition sum $\sum_{\{n_1..n_N\}}\exp(-\beta H)$. How is this different from the ideal gas, in which case I need the gibbs factor? | |
| Jun 18, 2020 at 8:30 | history | answered | user245141 | CC BY-SA 4.0 |