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Curvature depresses the equilibrium melting temperature of solid convex into liquid. Here $\mathcal{K}$ is the sum of principal curvatures, equal to twice a common convention for mean curvature, and $T_m$ is absolute temperature. The coefficient uses solid-liquid surface energy, mass density and latent heat. This stabilizes fine corrugations of a solidification front.

Along a reversible path at fixed volume, $dS=C_V(T)dT/T$. Hence entropy differences can be measured macroscopically fromwith an additional $L/T_c$ across a first-order transition of latent heat $L$ at $T_c$.

Freezing is a liquid-to-solid phase transition. A moving phase boundary releases latent heat; its rate is constrained by heat transport and the Stefan condition. In a solution the liquidus depends on composition, so being below the pure solvent's melting temperature does not imply that the solution must freeze.

A lava lake is a persistent exposed body of molten or partly molten magma. Surface radiative cooling, thermal convection, latent heat, and internal radiogenic heating can jointly control formation and melting of its crust.

Melting is a solid-to-liquid phase transition that absorbs latent heat. It can be driven by heating, changing phase pressures, or adding solute that causes freezing-point depression. The ice layer between freshwater and cold brine illustrates melting into a cold liquid through dilution and a composition-dependent liquidus.

Ocean heat content relative to a reference temperature $T_f$ is an integral through the water column. For a uniform column of depth $H$, $Q={\rho }_w{c}_{w}H(T-T_f)$ per horizontal area. Melting ice already at its fusion temperature requires its latent heat; warming cold ice first requires additional sensible heat. A surface temperature alone does not determine the column integral.