The theory of equilibrium fluctuations of thermodynamic quantities in open systems with a small number of particles

Fluctuations in open subsystems with a small number of particles and fixed volume immersed in an equilibrium system (thermostat) are treated. Within the framework of classical thermodynamics, the distribution functions of fluctuations of the number of particles, momentum, and energy in these subsystems are derived. These results are compared with the corresponding data obtained for hard spheres using the method of molecular dynamics. Their satisfactory agreement is observed. It is demonstrated that the distribution functions of fluctuations of the number of particles and energy are significantly different from both the Gauss and Poisson distribution. The distribution function of fluctuations of momentum of a small subsystem is Gaussian and independent of the density of the thermostat.