Microcanonical ensemble: Difference between revisions
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== Ensemble variables == | == Ensemble variables == | ||
(One component system, 3-dimensional system, ... ): | (One component system, 3-dimensional system, ... ): | ||
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== Partition function == | == Partition function == | ||
<math> Q_{NVE} = \frac{1}{h^{3N} N!} \int \int d (p)^{3N} d(q)^{3N} \delta ( H(p,q) - E). | :<math> Q_{NVE} = \frac{1}{h^{3N} N!} \int \int d (p)^{3N} d(q)^{3N} \delta ( H(p,q) - E). | ||
</math> | </math> | ||
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* <math> H \left(p,q\right) </math> represent the Hamiltonian, i.e. the total energy of the system as a function of coordinates and momenta. | * <math> H \left(p,q\right) </math> represent the Hamiltonian, i.e. the total energy of the system as a function of coordinates and momenta. | ||
*<math> \delta \left( x \right) </math> is the [[Dirac delta distribution | *<math> \delta \left( x \right) </math> is the [[Dirac delta distribution]] | ||
== Thermodynamics == | == Thermodynamics == | ||
: <math> \left. S = k_B \log Q_{NVE} \right. </math> | :<math> \left. S = k_B \log Q_{NVE} \right. </math> | ||
where: | where: | ||
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== References == | == References == | ||
# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press | # D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press | ||
[[Category:Statistical mechanics]] | |||
Revision as of 11:50, 27 February 2007
Ensemble variables
(One component system, 3-dimensional system, ... ):
- : Number of Particles
- : Volume
- : Internal energy (kinetic + potential)
Partition function
where:
- is the Planck constant
- represents the 3N Cartesian position coordinates.
- represents the 3N momenta.
- represent the Hamiltonian, i.e. the total energy of the system as a function of coordinates and momenta.
- is the Dirac delta distribution
Thermodynamics
where:
- is the entropy
- is the Boltzmann constant
References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press