The paper (Sibik, J.; Elliott, S. R.; Zeitler, J. A. J. Phys. Chem. Lett. 2014, 5, 19681972) used terahertz time-domain spectroscopy (THz-TDS) to study the dynamics of the polyalcohols, glycerol, threitol, xylitol, and sorbitol, at temperatures from below to above the glass transition temperature T-g. On heating the glasses, they observed the dielectric losses, epsilon ''(nu) at nu = 1 THz, increase monotonically with temperature and change dependence at two temperatures, first deep in the glassy state at T-THz = 0.65T(g) and second at T-g. The effects at both temperatures are most prominent in sorbitol but become progressively weaker in the order of xylitol and threitol, and the sub-T-g change was not observed in glycerol. They suggested this feature originates from the high-frequency tail of the Johari-Goldstein (JG) beta-relaxation, and the temperature region near 0.65T(g) is the universal region for the secondary glass transition due to the JG beta-relaxation. In this paper, we first use isothermal dielectric relaxation data at frequencies below 10(6) Hz to locate the "second glass transition" temperature T-beta at which the JG beta-relaxation time tau(JG) reaches 100 s. The value of T-beta is close to T-THz = 0.65T(g) for sorbitol (0.63T(g)) and xylitol (0.65T(g)), but T-beta is 0.74T(g) for threitol and 0.83T(g) for glycerol. Notwithstanding, the larger values of T-beta of glycerol are consistent with the THz-TDS data. Next, we identify the dynamic process probed by THz-TDS as the caged molecule dynamics, showing up in susceptibility spectra as nearly constant loss (NCL). The caged molecule dynamics regime is terminated by the onset of the primitive relaxation of the coupling model, which is the precursor of the JG beta-relaxation. From this relation, established is the connection of the magnitude and temperature dependence of the NCL and those of tau(JG). This connection explains the monotonic increase of NCL with temperature and change to a stronger dependence after crossing T-beta giving rise to the sub-T-g behavior of epsilon ''(nu) observed in experiment. Beyond the polyalcohols, we present new dielectric relaxation measurements of flufenamic acid and recall dielectric, NMR, and calorimetric data of indomethacin. The data of these two pharmaceuticals enables us to determine the value of T-beta = 0.67T(g) for flufenamic acid and T-beta = 0.58T(g) or T-beta = 0.62T(g) for indomethacin, which can be compared with experimental values of TTHz from THz-TDS measurements when they become available. We point out that the sub-T-g change of NCL at T-beta found by THz-TDS can be observed by other high frequency spectroscopy including neutron scattering, light scattering, Brillouin scattering, and inelastic X-ray scattering. An example from neutron scattering is cited. All the findings demonstrate the connection of all processes in the evolution of dynamics ending at the structural alpha-relaxation.