Microcanonical ensemble: Difference between revisions
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* <math> \left. V \right. </math>: is the volume | * <math> \left. V \right. </math>: is the volume | ||
* <math> \left. E \right. </math>: is the internal energy (kinetic + potential) | * <math> \left. E \right. </math>: is the [[internal energy]] (kinetic + potential) | ||
== Partition function == | == Partition function == |
Revision as of 17:52, 5 March 2007
Ensemble variables
(One component system, 3-dimensional system, ... ):
- : number of particles
- : is the volume
- : is the internal energy (kinetic + potential)
Partition function
where:
- is the Planck constant
- represents the 3N Cartesian position coordinates.
- represents the 3N momenta.
- represents 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