Timeline for How do you derive the Maxwell-Boltzmann distribution?
Current License: CC BY-SA 4.0
24 events
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| Oct 23, 2021 at 13:02 | history | edited | Qmechanic♦ |
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| Oct 22, 2021 at 19:51 | comment | added | Connor | @bolbteppa A very late response, but it's intuitive to me as $-log(\frac{N_i}{N}) = log(\frac{N}{N_i})$ gets larger for single particle microstates that have low numbers of particles, which fits the expression on the right hand side which gets larger as the energy you're searching for gets larger for some fixed temperature. Perhaps we mean different things by intuitive, I mean the equation makes sense to me. | |
| Sep 16, 2021 at 22:30 | comment | added | bolbteppa | How is the upper equation $-\log\Big(\frac{N_i}{N}\Big) \propto \frac{E_i}{T}$ intuitive to you? This, as the wiki says, comes from Maxwell-Boltzmann statistics, meaning the derivation of the Boltzmann distribution, the setting up of which is the 'hardest' part of the whole derivation, are you sure you appreciate where it comes from? | |
| Sep 14, 2021 at 2:23 | comment | added | user1379857 | This is maybe a bit of self promotion but I one wrote a note that proves it with very little overhead. scholar.harvard.edu/files/noahmiller/files/… | |
| Sep 14, 2021 at 2:20 | answer | added | ytlu | timeline score: 1 | |
| Sep 13, 2021 at 23:52 | comment | added | Claudio Saspinski | There is a course of statistical mechanics in youTube with 10 videos, from prof. Leonard Susskind. That derivation is well done there. | |
| Sep 13, 2021 at 21:32 | comment | added | Michael Seifert | I'm unfamiliar with that particular book, I'm afraid. | |
| Sep 13, 2021 at 21:31 | comment | added | Connor | @MichaelSeifert Thanks! I am currently looking at Stephen Blundell's book "Concepts in Thermal Physics" which seems to be of a similar level, except the topics are split into smaller groups. Have you heard of it? How do you think it compares? | |
| Sep 13, 2021 at 21:30 | history | edited | Michael Seifert | CC BY-SA 4.0 |
Posts should be confined to one question at a time. Feel free to post a separate question asking for resource recommendations for learning statistical physics
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| Sep 13, 2021 at 21:28 | comment | added | Michael Seifert | @Connor: A common undergraduate text in the US is Schroeder's An Introduction to Thermal Physics. It's highly readable and probably good for self-study. The author assumes that the reader has taken "a year-long introductory physics course and a year of calculus", though multi-variable calculus is immensely helpful as well. Boltzmann statistics (which is what you want) is in Chapter 6; you'll probably need to read Chapters 1–3 before you dive into that, though. | |
| Sep 13, 2021 at 19:40 | comment | added | Connor | @Wolphramjonny Okay, thank you anyway, I will try and find a derivation and then update this thread with my own answer. I think it's important a good (thorough/ complete) derivation is easily searchable, with a physical explanation! | |
| Sep 13, 2021 at 19:35 | comment | added | user65081 | Unfortunately I do not remember well enough to advice you on that, it has been a very long time since I studied this subject | |
| Sep 13, 2021 at 19:29 | comment | added | Connor | @Wolphramjonny Let's say I have an understanding of Undergraduate mathematics up to what is required for the average statistical mechanics course. What would be a good book on that level? | |
| Sep 13, 2021 at 19:00 | comment | added | user65081 | Every demonstration will skip some steps, that you are assumed to know if you are reading at that level. Otherwise books would become extremely long, and boring too | |
| Sep 13, 2021 at 18:55 | review | Close votes | |||
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| S Sep 13, 2021 at 18:49 | history | suggested | Lorenzo B. | CC BY-SA 4.0 |
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| Sep 13, 2021 at 18:48 | comment | added | Connor | @BySymmetry Okay, that sort of makes sense, could you explain how one uses that to move from the upper relation, to the lower equation? Or are the two not as related as the Wikipedia article implies? In what sense is the Boltzmann constant related to the normalising factor? Thanks! | |
| Sep 13, 2021 at 18:44 | review | Suggested edits | |||
| S Sep 13, 2021 at 18:49 | |||||
| Sep 13, 2021 at 18:39 | comment | added | By Symmetry | The normalization simply comes from the fact that $N = \sum_i N_i$ | |
| Sep 13, 2021 at 18:36 | comment | added | Connor | @Roger Vadim What is you favourite example of such a book for simplicity of derivation with no skipped steps or assumed knowledge? | |
| Sep 13, 2021 at 18:35 | comment | added | Roger V. | It is derived in every statistical physics textbook. | |
| Sep 13, 2021 at 18:21 | history | edited | Connor | CC BY-SA 4.0 |
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| S Sep 13, 2021 at 18:14 | review | First questions | |||
| Sep 13, 2021 at 18:28 | |||||
| S Sep 13, 2021 at 18:14 | history | asked | Connor | CC BY-SA 4.0 |