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Molecular Dynamics (MD) simulations were carried out in a microcanonical ensemble to compute the Gruneisen parameter (denoted as γ) of a liquid of bead-spring chains having 10 beads/chain. γ was studied over a wide range of temperatures below and above the glass transition temperature. We found that the Gruneisen parameter varied in the range of 2.1-3.1 and was significantly higher than typically observed experimentally in real polymers. In the glass, a theory was developed for γ using a cell model in which the beads are harmonically b