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A thermodynamic theory has been developed to calculate the shock temperature of polymers in the 1 GPa pressure region. For this purpose, the Grüneisen parameter has been calculated based on the available nonlinear shock velocity–particle velocity Hugoniot function for polymers. The calculated large values of the parameter correspond to that of phonon frequencies in the collective motion of polymer molecules, and not to that of the intramolecular vibration frequencies. Then, the equilibrium shock temperature as well as the cold potential energy function is calculated using the calculated Grüneisen parameter and the available nonlinear shock velocity–particle velocity Hugoniot function. Shock temperature and cold potential function have also been calculated using the equilibrium thermodynamic values of the Grüneisen parameter and the specific heat. From these calculations, the following unphysical result has been derived; that is, the cold potential function for these polymers has no minimum value at zero-temperature volume, but monotonically decreases with compression. It is demonstrated that this kind of anomaly can be resolved only when large values of the Grüneisen parameter and the corresponding small values of the specific heat are assumed. These results strongly suggest that the state of the shocked polymers observed in the experiment of μs duration may be the thermodynamic state, which is very different from the thermal equilibrium state in that phonon temperature is sufficiently high but not in equilibrium with molecular vibrational temperature. © 1998 American Institute of Physics.