The spontaneous decrease of the enthalpy and entropy of the variously vitrified 2-methyl-3-heptanol, an octanol isomer which behaves like a nonpolar liquid as its molecular dipole vectors mutually cancel on intermolecular hydrogen bonding, has been studied by differential scanning calorimetry. The effect of annealing for different periods at a fixed temperature, and at different temperatures for a fixed period, has been investigated. The structural relaxation is close to exponential, and its characteristic time, in contrast with other glasses, does not increase with the annealing time. These characteristics are different from those found for other materials and correspond to a first-order rate of a chemical process or an exponential decay of the thermal functions. The exponential character and the low activation energy (=37.7 kJ/mol) of the process, which is comparable to the energy for the formation of two H-bonds and to the enthalpy (-36 kJ/mol) of ring dimerization data available in the literature, indicate that the enthalpy decrease observed on annealing is mainly a reflection of an increase in the concentration of the nonpolar ring dimers formed by H-bond association. The effect is attributed to the increase in the reaction quotient toward the equilibrium constant value of the intermolecular hydrogen-bond association reaction in the liquid’s structure, as the fictive temperature decreases. The increase in the number of H-bonds and in the reaction quotient, as it approaches the equilibrium constant for the reaction, monomer <----> ring dimer or lineardimer <----> ring dimer, as well as the equilibrium concentration of the dimers, has been calculated from the enthalpy and entropy decrease observed on annealing. This is combined with a similar calculation from the dielectric data available in the literature. It is proposed that such effects occur also in materials with abundant H-bonding, as in hydrated proteins and carbohydrates and those in which ion association and isomerization reactions occur, and that the availability of configurational and conformational degrees of freedom is necessary for their occurrence. Hence, we introduce the terms for discussing spontaneous enthalpy and entropy decrease of an H-bonded glass in terms of a chemical fictive temperature corresponding to the H-bond and ion-pair formation.