Inherent noise present in molecular dynamics simulations and what can be learnt from it for 2D Lennard–Jones system

We have investigated the influence of finite number of particles used in molecular dynamics simulations on the fluctuations of thermodynamic properties. As a case study, the two-dimensional Lennard–Jones system was used. The 2D Lennard–Jones is an archetypal system and a subject of long debate about whether it has continuous (infinite-order) or discontinuous (the first-order) melting transition. We have found, that anomalies on the equation of state (the van-der-Waals or Myer–Wood loops), previously considered a hallmark of the first order phase transition, are at best at the level of noise, since their magnitude is the same as the amplitude of pressure fluctuations. So, they could be regarded as a statistically unsignificant effect. Also, we estimated inherent statistical noise present in computer simulations, and came to the conclusion, that it is larger than predicted by statistical physics, and the difference between them (called algorithmic fluctuations) may be due to the computer-related issues.