Microcanonical ensemble

Microcanonical Ensemble (Clasical statistics):

Ensemble variables

(One component system, 3-dimensional system, ... ):

• $\left.N\right.$: Number of Particles

• $\left.V\right.$: Volumne

• $\left.E\right.$: Internal enerrgy (kinetic + potential)

Partition function

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Q_{NVE}={\frac {1}{h^{3N}N!}}\int \int d(p)^{3N}d(q)^{3N}\delta (H(p,q)-E).}

where:

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left.h\right.} is the Planck constant

• Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \left(q\right)^{3n}} represents the 3N Cartesian position coordinates.

• $\left(p\right)^{3n}$ represents the 3N momenta.

• $H\left(p,q\right)$ represent the Hamiltonian, i.e. the total energy of the system as a function of coordinates and momenta.

• $\delta \left(x\right)$ is the Dirac delta function

References

1. D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press