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Kenneth G. Libbrecht analyzes ice growth and frost heave using thermodynamics. His heat-engine argument bounds the overburden pressure that an advancing freezing front can sustain by comparing useful mechanical work with the maximum efficiency allowed between warm and cold reservoirs.^[ref]

The method separates an equilibrium upper bound from the actual growth rate. A thermodynamically permitted pressure need not be reached if liquid supply or heat removal is too slow. Frost heave therefore cannot be understood solely as the volume expansion of an isolated water sample on freezing.

Thermomolecular pressure is the force per area transmitted through a thin premelting liquid film between a solid and a substrate. Let $d$ be film thickness. For a repulsive, nonretarded dispersion interaction, define a positive interaction amplitude $A$ byThis sign convention assigns positive $p_T$ to repulsion; a signed Hamaker constant in another convention must be translated before using this formula. The strong thickness dependence permits a thin film to support appreciable load while remaining hydraulically connected to a liquid supply.

In the equal-phase-density approximation, the Clapeyron pressure relation for equal-density phases gives $p_s-p_l\simeq \rho L(T_m-T_i)/T_m$. A molecular film force can balance this phase-pressure difference and an applied load. With $\rho \simeq 10^3\mathrm{kg}{\mathrm{m}}^{-3}$, $L\simeq 3.34\times 10^5\mathrm{J}\mathrm{k}{\mathrm{g}}^{-1}$ and $T_m\simeq 273\mathrm{K}$, an undercooling of $0.1\mathrm{K}$ corresponds to a pressure scale about $0.12\mathrm{MPa}$. This is an equilibrium driving or limiting scale, not a guaranteed growth rate; liquid delivery through Darcy flow can limit frost heave.^[ref]