We have used molecular dynamics to simulate various systems of polymer chains and Lennard-Jones molecules; the neighboring monomers along a polymer chain are connected by rigid bonds or spring of strength k spring . We find that the velocity distributions of monomers in a wide range of simulation time can be well described by Tsallis q-statistics [C. Tsallis, J. Stat. Phys. 52 (1988) , 479] (q ≥ 1) and a single scaling function; the value of q is related to the conformation constraining

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... l, the interactions with background fluid, the destruction of chain homogeneity or the value of k spring ; when q → 1, the velocity distribution of monomers becomes Maxwell-Boltzmann distribution. We also find that the polymer chains tend to aggregate as neighboring monomers of a polymer chain have small or zero bending-angle and torsion-angle dependent potentials. The implication of our results for the aggregation of proteins is discussed.