On the problem of thermodynamic fluctuations in computer simulations

We discuss two approaches to studying thermodynamic fluctuations in computer simulations. The first is based on the theory presented in Landau and Lifshitz's textbook, which assumes a self-consistent solution to the problem, and the second, developed by Lebowitz–Percus–Verlet, et al., is suitable for a limited class of computer simulations based on the classical method of molecular dynamics. The study of fluctuations in a molecular dynamics simulation of helium fluid at room temperature and a pressure of 2 kbar reveals that they differ by several times depending on the type of ensemble (NVE or NVT) used in the computations. For the NVT ensemble, the best result is given by the Landau–Lifshitz approach, and for the microcanonical NVE ensemble, by the Lebowitz–Percus–Verlet approach. At the same time, the NVT ensemble in this system is shown to have a distribution density of temperature fluctuations different from the normal one. This difference is associated with the presence of so-called algorithmic fluctuations caused by the computer implementation of the calculation algorithm: discreteness of time, limited computation time, etc. The fundamental possibility of reconciling the weakly conservative laws of particle motion, where energy is conserved on average, with the manifest asymmetry of the time evolution of the system as a whole is demonstrated.