Molecular dynamics simulation of gas models of Lennard-Jones type interactions: Extensivity associated with interaction range and external noise

Statistics of a two-dimensional gas model interacting through a Lennard-Jones type potential, is considered. The goal is to examine the extensivity of internal energy in respect to the potential range and external white noise through molecular dynamics simulation. Accordingly a molecular dynamics simulation model is designed that provides reasonable evidence, in this respect. It is shown that for the long range potential the internal energy scales according to non-extensive thermodynamics expectation and the criteria is specified. Besides, for the short range case we demonstrate that the external noise drastically modifies the statistics of gas and makes the internal energy non-extensive. The relation between the non-extensive parameter, q, and the relaxation time and the noise intensity is obtained.