Fluctuations confined to local regions in the structure of a glass are observed as the Johari-Goldstein (JG) relaxation. Properties of these regions and their atomic configuration are currently studied by relaxation techniques, by electron microscopy, and by high-energy X-ray scattering and extended x-ray absorption fine structure methods. One expects that these fluctuations (i) would kinetically freeze on cooling a glass, and the temperature coefficient of its enthalpy, dH/dT, would consequently show a gradual decrease with decrease in T, (ii) would kinetically unfreeze on heating the glass toward the glass-liquid transition temperature, Tg, and dH/dT would gradually increase, and (iii) there would be a thermal hysteresis indicating the time and temperature dependence of the enthalpy. Since no such features have been found, thermodynamic consequences of these fluctuations are debated. After searching for these features in glasses of different types, we found it in one of the most stable metal alloy glasses of composition Pd40Ni10Cu30P20. On cooling from its Tg, dH/dT decreased along a broad sigmoid-shape path as local-region fluctuations kinetically froze. On heating thereafter, dH/dT increased along a similar path as these fluctuations unfroze, and there is hysteresis in the cooling and heating paths, similar to that observed in the Tg-endotherm range. After eliminating other interpretations, we conclude that local-region fluctuations seen as the JG relaxation in the non-equilibrium state of a glass contribute to its entropy, and we suggest conditions under which such fluctuations may be observed.