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A good conceptual starting point is to like the example that is mentioned at The Harvest of a Century by Siegmund Brandt (2008).
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Consider a system with 2 particles and 3 states. Remember that:
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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
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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.....
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Ancestors

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