Microcanonical ensemble: Difference between revisions
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m (New page: Microcanonical Ensemble (Clasical statistics): Ensemble variables (One component system, 3-dimensional system, ... ): * <math> \left. N \right. </math>: Number of Particles * <math> \le...) |
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Microcanonical Ensemble (Clasical statistics): | Microcanonical Ensemble (Clasical statistics): | ||
Ensemble variables (One component system, 3-dimensional system, ... ): | == Ensemble variables == | ||
(One component system, 3-dimensional system, ... ): | |||
* <math> \left. N \right. </math>: Number of Particles | * <math> \left. N \right. </math>: Number of Particles | ||
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* <math> \left. E \right. </math>: Internal enerrgy (kinetic + potential) | * <math> \left. E \right. </math>: Internal enerrgy (kinetic + potential) | ||
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). | ||
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where: | where: | ||
*<math> \left. h \right. </math> is | *<math> \left. h \right. </math> is the [[Planck constant]] | ||
*<math> \left( q \right)^{3n} </math> represents the 3N Cartesian position coordinates. | |||
... | *<math> \left( p \right)^{3n} </math> represents the 3N 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|Dirac delta function]] | |||
== References == | |||
# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press | |||
Revision as of 11:25, 27 February 2007
Microcanonical Ensemble (Clasical statistics):
Ensemble variables
(One component system, 3-dimensional system, ... ):
- : Number of Particles
- : Volumne
- : Internal enerrgy (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 function
References
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Alogrithms to Applications", Academic Press