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# Maxwell-Boltzmann vs Bose-Einstein vs Fermi-Diract statisics

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:
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.....