Partition function & Boltzman, Maxwell distri

[pivoxa15]

What is the relation between the partition function and the Boltzmann, Maxwell distribution?

Differences and similarities?

Both have exponentials to the power of the negative total energy of the microstate. Although the word microstate doesn't occur in the Boltzmann, Maxwell case.

Is the BM distribution about velocity and position of particles only whereas the partition function is about any distribution involving macro variables? So it cannot calculate the speeds and position of particles in the system but can tell you about energy, pressure, temperture etc.

 

[smallphi]

The normalization constant of the energy probability distribution of a system is one over the partition function.

In the MB distribution, the system is a single particle in the heat bath of all the rest. The microstates are that particle at different energies (kinetic + potential if any).

 

[pivoxa15]

So the MB is a more specialised or more restricted entity? Could you use the partition function to calculate position and velocity of particles?

 

[smallphi]

The MB distributions are derivable from the energy probability distribution. In fact they are the same thing written in different variables:

http://en.wikipedia.org/wiki/Maxwell–Boltzmann_distribution

 

[pivoxa15]

Interesting but you can't derive the partition function from the MB?

If you had non gas with potential energy than you would replace E=p^2/(2m) with K+U?

Then you would get the more general MB disbribution.