Microcanonical ensemble

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[edit] Ensemble variables

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

  • \left. N \right. : number of particles
  • \left. V \right. : is the volume

[edit] Partition function

Q_{NVE} = \frac{1}{h^{3N} N!} \iint d (p)^{3N} d(q)^{3N} \delta ( H(p,q) - E).

where:

  • \left( q \right)^{3N} represents the 3N Cartesian position coordinates.
  • \left( p \right)^{3N} represents the 3N momenta.
  • H \left(p,q\right) represents the Hamiltonian, i.e. the total energy of the system as a function of coordinates and momenta.

[edit] Thermodynamics

\left. S = k_B \log Q_{NVE} \right.

where:

[edit] References

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