What statistical models describe physical systems and when to use them?

[mezarashi]

I understand that there are a couple of statistical models out there that describe physical systems. One I know is Fermi-Dirac statistics. What are the other models, what are their key features and when are they applied? When working with a system, how can you be sure you should be using this particular model.

Any clues on how these models "derived" if they were at all. Thanks for your input ^^

 

[mathman]

The two principal statistics describing particles at the atomic level are Fermi-Dirac and Bose-Einstein. The F-D describe particles with half integer spin (electrons, protons, neutrons,etc.), while B-E describe particles of integer spin (H1 atoms, photons, etc.). One major (maybe the most important) difference between them is that F-D particles obey the Pauli exclusion principle, i.e. only one particle may be in a given state (the standard description of electrons in atoms results from this), while B-E particles do not (leading to experiments involving B-E condensates - you can look it up).