Microcanonical ensemble: Difference between revisions
Jump to navigation
Jump to search
Line 21: | Line 21: | ||
*<math> \left( p \right)^{3N} </math> represents the 3N momenta. | *<math> \left( p \right)^{3N} </math> represents the 3N momenta. | ||
* <math> H \left(p,q\right) </math> | * <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. | ||
*<math> \delta \left( x \right) </math> is the [[Dirac delta distribution]] | *<math> \delta \left( x \right) </math> is the [[Dirac delta distribution]] |
Revision as of 15:49, 28 February 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