# What is the meaning of non-degenerate in statistical mechanics?

• ck00

#### ck00

why do we say that a classically behaved gas is non-degenerate and a quantum behaved gas is degenerate?
I can't get why the word of "degeneracy" here can distinguish two kinds of behavior of gas.

does anyone know it?

http://farside.ph.utexas.edu/teaching/qmech/lectures/node65.html

This website is a great resource for physics students (like me). Here, he basically shows that we call matter "degenerate" if the Pauli Exclusion Principle is the main source of the pressure of the matter. Two identical fermions, such as electrons, can't be in the same quantum state at the same time. If this resistance to being in the same state is the main thing keeping the electrons apart, then the electron gas is behaving like a degenerate gas.

I completely disagree with nucl34rgg btw since a gas of bosons (which obviously doesn’t fallow the Pauli exclusion principle) can be degenerate. I advise you to check out the Degenerate Matter page on Wikipedia.

## 1. What does "non-degenerate" mean in statistical mechanics?

In statistical mechanics, non-degenerate refers to a system in which there is no overlap between the energy levels of different particles. This means that each energy level is occupied by only one particle, and there are no multiple particles in the same energy state.

## 2. How does degeneracy affect statistical mechanics?

Degeneracy, or the presence of multiple particles in the same energy level, can significantly affect the behavior of a system in statistical mechanics. It can lead to unexpected correlations and interactions between particles, and can also affect the overall energy distribution of the system.

## 3. Is degeneracy always a problem in statistical mechanics?

No, degeneracy is not always a problem in statistical mechanics. In some cases, degeneracy can actually be beneficial, as it can lead to more stable energy states and promote certain types of behavior in the system.

## 4. How is non-degeneracy related to entropy in statistical mechanics?

In statistical mechanics, non-degeneracy is closely related to entropy, which is a measure of the disorder or randomness of a system. Non-degenerate systems have lower entropy, as there is less uncertainty about the energy levels and positions of particles.

## 5. Can degeneracy be controlled or manipulated in statistical mechanics?

Yes, degeneracy can be controlled and manipulated in statistical mechanics through various methods such as changing the temperature or external conditions of the system. This can have significant effects on the behavior and properties of the system, making it an important aspect to consider in research and applications.