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
- \( \left. E \right. \): is the internal energy (kinetic + potential)
[edit] Partition function
\[ Q_{NVE} = \frac{1}{h^{3N} N!} \iint d (p)^{3N} d(q)^{3N} \delta ( H(p,q) - E). \]
where:
- \( \left. h \right. \) is the Planck constant
- \( \left( q \right)^{3N} \) 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.
- \( \delta \left( x \right) \) is the Dirac delta distribution
[edit] Thermodynamics
\[ \left. S = k_B \log Q_{NVE} \right. \]
where:
- \( \left. S \right. \) is the entropy.
- \( \left. k_B \right. \) is the Boltzmann constant
[edit] References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press
