jats:titleAbstract</jats:title>jats:pEnhanced fluctuations pervade a phase near a transition point. This phenomenon was observed in recent simulations of polyhedral particles, where rod-shaped vacancy defects diffused through a solid phase carrying mass flow. The defects proliferated at the melting point, magnifying the mass flow to liquid proportions. Here, we show that the number of vacancies increases on heating or lowering the pressure, in accordance with Boltzmann statistics, but the Boltzmann equilibrium becomes unstable at a threshold number resulting in the first-order melting transition. The instability is driven by an increase in entropy if the defects repel, or by a reduction in enthalpy if they attract. A corresponding thermodynamic instability occurs in other melting transitions, including in argon, colloids, cryogenic helium and simulations of hard spheres. The statistics of the vacancies explains a long-standing anomaly in the heat capacity of solid helium-4, as well as recent measurements of thermally activated mass flow through solid helium-3. In liquid helium-4, the vacancies conform to Feynman’s atomistic and quantum descriptions of rotons and quantitatively account for associated neutron scattering measurements. Colloids, silicon and sodium also melt ‘re-entrantly’ on elevating the pressure, and we identify quantitative evidence that this transition involves the proliferation of interstitial defects.</jats:p>