From nonlinear oscillations to equation of state in simple discrete systems

Nonlinear oscillations of a single particle in the potential well and for one-dimensional chain of interacting particles are considered. The law of interaction is of Lennard-Jones type, mimicking interaction in atomic systems. Similarities in average behaviour of the systems with one and many degrees of freedom are shown. Time averaging for the random oscillations is used to obtain thermodynamic characteristics such as pressure, specific volume, and thermal energy. Second order equation of state is obtained, which is valid in the conditions of strong extension, where fails the widely used Mie–Grüneisen equation of state.