Recently, a methodology to derive an exactly-solvable Riccati equation that approximates the macroscopic-phenomenological behavior of amorphous polymers at glass transition during isobaric cooling was introduced [C.Corbisieri, Macromol. Theory Simul. 33 (2024): 2400052]. In the present work, this methodology is applied to derive a closed-form expression in terms of mathematical functions that describes the pressure derivative of the specific volume during isothermal compression. For this purpose, a relation between the compression rate and relaxation time at glass transition pressure, 𝑃𝑔, formally identical to the Frenkel–Kobeko–Reiner equation, is postulated. The closed-form expression contains the logistic function, thus featuring a continuous transition region centered around the temperature and compression-rate dependent glass transition pressure. The resulting constitutive model well-fits the pressure-volume-temperature data of polycarbonate in the equilibrium state, the vitreous state, and at glass transition, collected in the standard isothermal mode in the pressure range 𝑃 = 10 MPa to 200 MPa at temperatures 𝑇₀ = {285, 265,…, 65}°C. This work thus confirms the validity of the logistic function in glass transition models of amorphous polymers and establishes a theoretical framework to assess the glass transition during isothermal compression.