Partition function & Boltzman, Maxwell distri

In summary, the partition function and the Boltzman, Maxwell distribution both involve exponentials to the power of the negative total energy of the microstate. However, the Boltzman, Maxwell distribution does not mention the word "microstate." The Boltzman, Maxwell distribution is focused on the velocity and position of particles, while the partition function can calculate energy, pressure, temperature, and other macro variables. The normalization constant of the energy probability distribution is one over the partition function. The MB distribution is a specialized version of the energy probability distribution, where the system is a single particle in a heat bath. The microstates in the MB distribution represent the particle at different energies. The partition function cannot be derived from the MB distribution, but the MB distribution
  • #1
pivoxa15
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What is the relation between the partition function and the Boltzman, Maxwell distribution?

Differences and similarities?

Both have exponentials to the power of the negative total energy of the microstate. Although the word microstate dosen't occur in the Boltzman, 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.
 
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  • #2
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).
 
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  • #3
So the MB is a more specialised or more restricted entity? Could you use the partition function to calculate position and velocity of particles?
 
  • #5
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.
 

What is the partition function?

The partition function is a mathematical concept used in statistical mechanics to describe the distribution of particles in a system. It is a sum of all possible states that a system can be in, weighted by their respective energies.

What is the Boltzmann distribution?

The Boltzmann distribution is a probability distribution that describes the distribution of particles in a system at thermal equilibrium. It is derived from the partition function and is used to calculate the probability of a particle being in a certain energy state.

How is the partition function related to thermodynamic properties?

The partition function is related to thermodynamic properties such as internal energy, entropy, and free energy. These properties can be calculated from the partition function by using mathematical relationships known as the partition function identities.

What is the Maxwell distribution?

The Maxwell distribution is a probability distribution that describes the speeds of particles in a gas at a given temperature. It is derived from the Boltzmann distribution and is used to calculate the average speed of particles in a gas.

How is the partition function used in quantum mechanics?

In quantum mechanics, the partition function is used to calculate the average energy of a system. It is also used to calculate thermodynamic properties such as heat capacity and chemical potential, and is an essential tool in understanding the behavior of quantum systems.

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