The definitions of breaks and clusters in a one-dimensional chain in equilibrium are discussed. Analytical expressions are obtained for the expected cluster length, $langle K rangle$, as a function of temperature and pressure in a one-dimensional Lennard-Jones chain. These expressions are compared with results from molecular dynamics simulations. It is found that $langle K rangle$ increases exponentially with $beta = 1/k_BT$ and with pressure, $P$ in agreement with previous results in the literature. A method is illustrated for using $langle K rangle (beta, P)$ to generate a phase diagram for the Lennard-Jones chain. Some implications for the study of heat transport in Lennard-Jones chains are discussed.
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