Point in Phase Space and a Microstate

[SteveDC]

Currently learning about Statistical Mechanics and just wanted to check my understanding. Am I right in saying that a point in phase space is just a specific microstate of the system?

 

[DrClaude]

Only if the system consists of a single classical particle with no internal structure.

 

[SteveDC]

Okay, if then the system has large number 'N' of particles, does a point in phase space correspond to the coordinates and momenta of a single particle in that system and a microstate is a 'superposition' (not sure if that's the right word!) of all the points in phase space for that particular microstate?

 

[DrClaude]

I realize that I was not clear at all in my previous answer.

For a system with N particles, there is a difference depending on whether the particle are distinguishable or not. If they are distinguishable, then each point in the 6N-dimensional (in 3D) phase space is a microstate. If the particles are indistinguishable, different points in phase space that correspond to exchanging the labels of two of the particles will correspond to the same microsate.

 

[SteveDC]

Ah I see, thanks. Is this what leads to the Quantum treatment of statistical mechanics? Since I'm assuming the particles are in fact indistinguishable based on QM and the classical approach of assuming they're distinguishable would lead to an overcounting of microstates, which in turn affects macroscopic properties like entropy.

 

[DrClaude]

With classical particles, making them indistinguishable often only requires an additional factor to remove the overcounting of identical states. For quantum particles, you have an additional condition due to the Pauli principle, which for fermions means that no two can be in the same state.

 

[SteveDC]

Interesting - THanks again.