Correlations and fluctuations in monodimensional chains of Lennard-Jones oscillators

The time-averaged length and the length fluctuations of monodimensional chains of nonlinear oscillators at equilibrium could be expressed as functions of pressure and temperature. The same formulae can be considered for non-equilibrium states, acting as microscopic relations for the single oscillators in the chain.This paper discusses the validity of those relations for the chain length and its fluctuations, by using computer simulations of Lennard-Jones chains of $N$ oscillators under a temperature gradient and confined by a constant constraining force. We show that such relations are accurate under specific ranges of values for the quantities involved and are, to some extent, dependent on the number of particles in the chain.It turns out that the single-oscillator relations perform remarkably well across a broad and physically relevant range of non-equilibrium states. The insights gained in this work can help clarify non-equilibrium properties of monodimensional chains of oscillators and their relations with statistical mechanical distributions. This can help understand some properties of nanoscopic systems.