**Statistical Fluctuations Along the Lennard-Jones Melting Curve**

Patra Ramakanta 1, Heyes D.M. 2

1 Department of Economics, Royal Holloway

University of London, Egham, Surrey TW20 0EX, UK

E-mail: ramakanta.patra.2011@live.rhul.ac.uk2 Department of Physics, Royal Holloway

University of London, Egham, Surrey TW20 0EX, UK

E-mail: david.heyes@rhul.ac.uk

### DOI: 10.12921/cmst.2016.22.01.001

### Abstract:

Statistical fluctuations and correlations between thermodynamic properties along the fluid side of the melting line of the Lennard-Jones (LJ) are determined using Molecular Dynamics (MD) computer simulation. Linear regression, the Pearson coefficient and other statistical measures are calculated. The cross correlation between the configurational part of the pressure and potential energy, and the repulsive and attractive parts of the potential energy are focussed on. Regression plots show that at constant temperature and constant total energy the Weeks-Chandler-Andersen (WCA) decomposition of the Lennard-Jones repulsive and attractive potential energy components show a qualitative change along the melting line. At low temperature the two components are correlated, while they are anticorrelated in the high temperature limit. There is an intermediate temperature range in which the two potential energy components are effectively uncorrelated. The various fluctuation trends along the melting line were found to be weakly dependent on the force field used to generate the distribution of states, namely, the LJ potential, inverse power potential with exponent 12, and the repulsive term in the WCA decomposition of the LJ potential.

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