A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).

Consider a system with 2 particles and 3 states. Remember that:

- in quantum statistics (Bose-Einstein statistics and Fermi-Dirac statistics), particles are indistinguishable, therefore, we might was well call both of them
`A`

, as opposed to`A`

and`B`

from non-quantum statistics - in Bose-Einstein statistics, two particles may occupy the same state. In Fermi-Dirac statistics

Therefore, all the possible way to put those two particles in three states are for:

- Maxwell-Boltzmann distribution: both A and B can go anywhere:
State 1 State 2 State 3 AB AB AB A B B A A B B A A B B A - Bose-Einstein statistics: because A and B are indistinguishable, there is now only 1 possibility for the states where A and B would be in different states.
State 1 State 2 State 3 AA AA AA A A A A A A - Fermi-Dirac statistics: now states with two particles in the same state are not possible anymore:
State 1 State 2 State 3 A A A A A A

Both Bose-Einstein statistics and Fermi-Dirac statistics tend to the Maxwell-Boltzmann distribution in the limit of either:TODO: show on forumulas. TODO experimental data showing this. Please.....

- high temperature
- low concentrations

Most applications of the Maxwell-Boltzmann distribution confirm the theory, but don't give a very direct proof of its curve.

Here we will try to gather some that do.

Measured particle speeds with a rotation barrel! OMG, pre electromagnetism equipment?

- bingweb.binghamton.edu/~suzuki/GeneralPhysNote_PDF/LN19v7.pdf
- chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Thermodynamics_and_Chemical_Equilibrium_(Ellgen)/04%3A_The_Distribution_of_Gas_Velocities/4.07%3A_Experimental_Test_of_the_Maxwell-Boltzmann_Probability_Density

Is it the same as Zartman Ko experiment? TODO find the relevant papers.

edisciplinas.usp.br/pluginfile.php/48089/course/section/16461/qsp_chapter7-boltzman.pdf mentions

- sedimentation
- reaction rate as it calculates how likely it is for particles to overcome the activation energy

Start by looking at: Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Diract statisics.

Start by looking at: Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Diract statisics.

Bibliography:

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