To date, accurate description of the pressure-volume-temperature (PVT) behavior in the vitreous state and at glass transition, a key feature of valid simulation of the processing of amorphous polymers, has often been subject to limitations of theories and models. Consequently, only a few models that describe the PVT behavior of amorphous polymers with limited predictive capability are implemented in commercial software of polymer processing simulation. In our research, we utilize the concepts of thermodynamics of irreversible processes to overcome these limitations. The non-equilibrium nature of amorphous polymers in the vitreous state and at glass transition is accounted for by introducing internal state variables in addition to the natural state variables of the corresponding thermodynamic potential. A result of this research is the logistic model equation of state (LM EOS). Unlike standard PVT models such as Tait's EOS, the LM EOS accurately describes the PVT behavior of amorphous polymers in the equilibrium state, the vitreous state and at glass transition without dividing the temperature domain into multiple intervals. Therefore, discontinuities are eliminated, and no conditional statements that divide the temperature domain into intervals of different model ansatzes and different model parameter-values have to be implemented in software. The LM EOS is continuously differentiable with respect to temperature and pressure, thus allowing for determination of the thermal expansion coefficient and compressibility at any valid reference state. In conclusion, polymer processing simulation could benefit from implementation of the LM EOS in commercial software. It is worth noting that a procedure to identify the parameters of the LM EOS from experimental data is available. The logistic model ansatz can also be used to determine the pressure and cooling-rate dependent glass transition temperature from experimental data.