Perturbation Theories for the Thermodynamic Properties of Fluids and Solids

Overview of Computer Simulation Methods 61

From Equations 2.47 and 2.48, the probability density ρ(N, U) that the system has

N particles and total energy U can be written as follows:

ρ

(

N, U

)

=

D

(

N, U

)

e

β

(

μN−U

)



, (3.90)

where D(N, U) is the density of states (number of microstates per unit energy interval

in a system with N particles and energy U). Then, for T, V, and μ fixed, we can go

further by integrating over energy for each value of N, thus obtaining the probabil-

ity p(N) that the system has N particles. In computer simulation, this probability is

recorded as a histogram obtained from averaging over many independent samples

(Wilding 2001). In a