Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein.

[Clau]

If we have indistinguishable particles, we must use Fermi-Dirac statistics.
To Identical and indistinguishable particles, we use Bose-Einstein statistics.
And, to distinguishable classical particles we use Maxwell-Boltzmann statistics.

I have a system of identical but distinguishable particles, where the second level has a degeneracy.

I was reading at Wikipedia: "Degenerate gases are gases composed of fermions that have a particular configuration which usually forms at high densities."

My question is: Should I use Fermi-Dirac statistics in this case?

I'm confused. I was reading Reif and it seems that I should use Maxwell-Boltzmann just to nondegenerate gases. But if my system is made by distinguishable particles, it seems that I should use MB statistics.

 

[vanesch]

I'm not an expert on this and if I'm making an error, please correct me. But I thought that distinguishability is the key element, which determines that one should use the MB statistics. The MB statistics is ALSO a good approximation to the other distributions in certain limiting cases (such as dilute media), but I thought that if we deal with distinguishable components, that MB was exact. (the problem being, of course, that there do not exist systems of distinguishable elementary particles in nature)

 

[astrokreng]

I can clarify the use of statistics in different systems of particles. The three statistics you mentioned, Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein, are used to describe the behavior of particles in different physical systems.

Maxwell-Boltzmann statistics apply to distinguishable classical particles, meaning particles that can be distinguished from one another based on their properties such as mass, charge, or spin. This type of statistics is used to describe non-degenerate gases, where the particles do not interact with each other and their energy levels are not quantized.

Fermi-Dirac statistics, on the other hand, apply to identical and indistinguishable particles, also known as fermions. These particles have half-integer spin and follow the Pauli exclusion principle, which states that no two identical fermions can occupy the same quantum state simultaneously. This type of statistics is used to describe degenerate gases, where the particles are highly interacting and their energy levels are quantized.

Bose-Einstein statistics are also used for identical and indistinguishable particles, but in this case, the particles are bosons with integer spin. Unlike fermions, bosons can occupy the same quantum state simultaneously. This type of statistics is used to describe systems with a large number of bosons, such as a gas of photons or a Bose-Einstein condensate.

In your case, if your system consists of identical but distinguishable particles with a degenerate second level, you should use Bose-Einstein statistics. This is because the particles are identical and indistinguishable, but their degenerate level allows for multiple particles to occupy the same energy state, making them behave like bosons.

I hope this clarifies the use of statistics in different systems of particles. It is important to choose the appropriate statistics based on the properties and behavior of the particles in your system.