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| '''Microcanonical ensemble'''
| | Microcanonical Ensemble (Clasical statistics): |
| == Ensemble variables ==
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| (One component system, 3-dimensional system, ... ): | |
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| * <math> \left. N \right. </math>: number of particles
| | Ensemble variables (One component system, 3-dimensional system, ... ): |
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| * <math> \left. V \right. </math>: is the volume | | * <math> \left. N \right. </math>: Number of Particles |
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| * <math> \left. E \right. </math>: is the [[internal energy]] (kinetic + potential) | | * <math> \left. V \right. </math>: Volumne |
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| == Partition function ==
| | * <math> \left. E \right. </math>: Internal enerrgy (kinetic + potential) |
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| :<math> Q_{NVE} = \frac{1}{h^{3N} N!} \iint d (p)^{3N} d(q)^{3N} \delta ( H(p,q) - E).
| | Partition function |
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| | <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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| where: | | where: |
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| *<math> \left. h \right. </math> is the [[Planck constant]] | | *<math> \left. h \right. </math> is |
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| *<math> \left( q \right)^{3N} </math> represents the 3N Cartesian position coordinates.
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| *<math> \left( p \right)^{3N} </math> represents the 3N momenta.
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| * <math> H \left(p,q\right) </math> represents the [[Hamiltonian]], i.e. the total energy of the system as a function of coordinates and momenta.
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| *<math> \delta \left( x \right) </math> is the [[Dirac delta distribution]]
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| == Thermodynamics ==
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| :<math> \left. S = k_B \log Q_{NVE} \right. </math>
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| where:
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| *<math> \left. S \right. </math> is the [[Entropy|entropy]].
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| *<math> \left. k_B \right. </math> is the [[Boltzmann constant]]
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| == References ==
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| <references/>
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| ;Related reading
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| * D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press
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| * [http://dx.doi.org/10.1063/1.4931484 Philipp Schierz, Johannes Zierenberg and Wolfhard Janke "Molecular Dynamics and Monte Carlo simulations in the microcanonical ensemble: Quantitative comparison and reweighting techniques", Journal of Chemical Physics '''143''' 134114 (2015)]
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| [[Category:Statistical mechanics]]
| | ... in construction --- |