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We address the relaxation dynamics in hydrogen-bonded super-cooled liquidsnear the glass transition, measured via Broad-Band Dielectric Spectroscopy(BDS). We propose a theory based on decomposing the relaxation of themacroscopic dipole moment into contributions from hydrogen bonded clusters of$s$ molecules, with $s_{min}\le s \le s_{max}$. The existence of $s_{max}$ isdue to dynamical arrest and its value may depend on the cooling protocol and onthe aging time. The existence of $s_{max}$ is translated into a sum-rule on theconcentrations of clusters of size $s$. We construct the statistical mechanicsof the super-cooled liquid subject to this sum-rule as a constraint, toestimate the temperature-dependent density of clusters of size $s$. With atheoretical estimate of the relaxation time of each cluster we providepredictions for the real and imaginary part of the frequency dependentdielectric response. The predicted spectra and their temperature dependence arein accord with measurements, explaining a host of phenomenological fits likethe Vogel-Fulcher fit and the stretched exponential fit. Using glycerol as aparticular example we demonstrate quantitative correspondence between theoryand experiments. The theory also demonstrates that the $\alpha$ peak and the"excess wing" stem from the same physics in this material. The theory alsoshows that in other hydrogen -bonded glass formers the "excess wing" candevelop into a $\beta$ peak, depending on the molecular material parameters(predominantly the surface energy of the clusters). We thus argue that $\alpha$and $\beta$ peaks can stem from the same physics. Finally we address the BDS inconstrained geometries (pores) and explain why recent experiments on glyceroldid not show a deviation from bul k spectra.

Theory of Relaxation Dynamics in Glass-Forming Hydrogen-Bonded Liquids