Editing Microcanonical ensemble
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== Ensemble variables == | == Ensemble variables == | ||
(One component system, 3-dimensional system, ... ): | (One component system, 3-dimensional system, ... ): | ||
* <math> \left. N \right. </math>: | * <math> \left. N \right. </math>: Number of Particles | ||
* <math> \left. V \right. </math>: | * <math> \left. V \right. </math>: Volume | ||
* <math> \left. E \right. </math>: | * <math> \left. E \right. </math>: Internal energy (kinetic + potential) | ||
== Partition function == | == Partition function == | ||
:<math> Q_{NVE} = \frac{1}{h^{3N} N!} \ | :<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> \left. h \right. </math> is the [[Planck constant]] | *<math> \left. h \right. </math> is the [[Planck constant]] | ||
*<math> \left( q \right)^{ | *<math> \left( q \right)^{3n} </math> represents the 3N Cartesian position coordinates. | ||
*<math> \left( p \right)^{ | *<math> \left( p \right)^{3n} </math> represents the 3N momenta. | ||
* <math> H \left(p,q\right) </math> | * <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]] | ||
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where: | where: | ||
*<math> \left. S \right. </math> is the [[Entropy|entropy]] | *<math> \left. S \right. </math> is the [[Entropy|entropy]]· | ||
*<math> \left. k_B \right. </math> is the [[Boltzmann constant]] | *<math> \left. k_B \right. </math> is the [[Boltzmann constant]] | ||
== References == | == References == | ||
# D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press | |||
[[Category:Statistical mechanics]] | [[Category:Statistical mechanics]] | ||