Microcanonical ensemble
Microcanonical ensemble
Ensemble variables[edit]
(One component system, 3-dimensional system, ... ):
-
: number of particles
-
: is the volume
-
: is the internal energy (kinetic + potential)
Partition function[edit]
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[edit]
where:
is the entropy.
is the Boltzmann constant
References[edit]
- Related reading
- D. Frenkel and B. Smit, "Understanding Molecular Simulation: From Algorithms to Applications", Academic Press
- 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)