In titanium alloys, the $\omega$(hexagonal)-phase transformation has been categorized as either a diffusion-mediated isothermal transformation or an athermal transformation that occurs spontaneously via a diffusionless mechanism. Here we report a diffusionless isothermal $\omega$ transformation that can occur even above the $\omega$ transformation temperature. In body-centered cubic $\beta$-titanium alloyed with $\beta$-stabilizing elements, there are locally unstable regions having fewer $\beta$-stabilizing elements owing to quenched-in compositional fluctuations that are inevitably present in thermal equilibrium. In these locally unstable regions, diffusionless isothermal $\omega$ transformation occurs even when the entire $\beta$ region is stable on average so that athermal $\omega$ transformation cannot occur. This anomalous, localized transformation originates from the fluctuation-driven localized softening of $2/3{\left[111\right]}_{\beta }$ longitudinal phonon, which cannot be suppressed by the stabilization of $\beta$ phase on average. In the diffusionless isothermal and athermal $\omega$ transformations, the transformation rate is dominated by two activation processes: a dynamical collapse of ${\left\{111\right\}}_{\beta }$ pairs, caused by the phonon softening, and a nucleation process. In the diffusionless isothermal transformation, the $\omega$-phase nucleation, resulting from the localized phonon softening, requires relatively high activation energy owing to the coherent $\beta /\omega$ interface. Thus, the transformation occurs at slower rates than the athermal transformation, which occurs by the widely spread phonon softening. Consequently, the nucleation probability reflecting the $\beta /\omega$ interface energy is the rate-determining process in the diffusionless $\omega$ transformations.

Many of the macroscopic properties of a glass are determined by the degree of structural relaxation. When the nonequilibrium system ages toward a thermodynamically more favorable state, the accompanying densification leads to an increase of the activation energies found for the $\alpha$ and especially the $\beta$ relaxation processes. In this work we experimentally quantify the low-energy mechanical relaxation spectrum of a metallic glass at cryogenic temperatures, and show that these relaxation processes intriguingly show the opposite trend. The energy scale as well as the relaxation strength decrease during the aging process below the glass transition temperature with a surprisingly strong dependence on the annealing time. The experimental results are analyzed in the framework of established models and the temporal behavior of the typical energy $V_0$ is assessed. We compare the derived values to the values of the thermal energy available at the estimated fictive temperature of the given state and find that the absolute values as well as their temporal behavior show a high degree of correlation for the studied metallic glass. The decreasing characteristic energy values found in the present experiment directly depict the evolution of the structure toward a hypothetical lowest entropy state before the glass becomes structurally indistinguishable from a crystalline material.