Fluctuations in an equilibrium hard-disk fluid: Explicit size effects

Explicit size corrections in the calculation of the fluctuations in the number of particles in a finite subvolume of a hard-disk fluid composed of a fixed number of particles are considered. The size corrections are obtained on the basis of a Taylor series expansion of the pair distribution function of the N-particle system in powers of 1/N. Analytical density dependent expressions are obtained at low density. These expressions show that not only explicit size effects (due to consideration of a fixed number of particles) but also edge effects that result from considering a finite subvolume must be taken into account. A general density dependence study is also reported by relating the relative fluctuation in the number of particles to the equation of state. Numerical results for the Henderson equation of state are obtained. These theoretical results are compared with Monte Carlo computer simulation results.