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We investigated the influence of a finite number of computer simulations bymolecular dynamics method on fluctuations in thermodynamic properties. As acase study, we used the two-dimensional Lennard-Jones system. Besides being anarchetypal system, the 2D Lennard-Jones system is a subject of long debate, asto whether its melting transition is continuous (infinite-order) ordiscontinious ( first-order) one. We have discovered that anomalies on theequation of state (the van-der-Waals or Myer-Wood loops) previously considereda hallmark of first order phase transition, are at best at the level of noise,since they have the same magnitude as the amplitude of pressure fluctuations.Having calculated the dependence of temperature fluctuations on the number ofparticles, we obtained another strong evidence of continuous character of thismelting transition, which manifests itself in continuous change of heatcapacity across the melting curve. We also compared the results obtained fortemperature fluctuations with prediction made by statistical mechanics .

How precise molecular dynamic simulations are and what we can learn from it?