  MESSENGER observations suggest a magma ocean formed on proto-Mercury, during
which evaporation of metals and outgassing of C- and H-bearing volatiles
produced an early atmosphere. Atmospheric escape subsequently occurred by
plasma heating, photoevaporation, Jeans escape, and photoionization. To
quantify atmospheric loss, we combine constraints on the lifetime of surficial
melt, melt composition, and atmospheric composition. Consideration of two
initial Mercury sizes and four magma ocean compositions determine the
atmospheric speciation at a given surface temperature. A coupled
interior-atmosphere model determines the cooling rate and therefore the
lifetime of surficial melt. Combining the melt lifetime and escape flux
calculations provide estimates for the total mass loss from early Mercury. Loss
rates by Jeans escape are negligible. Plasma heating and photoionization are
limited by homopause diffusion rates of $\sim10^{6}$ kg/s. Loss by
photoevaporation depends on the timing of Mercury formation and assumed heating
efficiency and ranges from $\sim10^{6.6}$ to $\sim10^{9.6}$ kg/s. The material
for photoevaporation is sourced from below the homopause and is therefore
energy-limited rather than diffusion-limited. The timescale for efficient
interior-atmosphere chemical exchange is less than ten thousand years.
Therefore, escape processes only account for an equivalent loss of less than
2.3 km of crust ($0.3\%$ of Mercury's mass). Accordingly, $\leq0.02\%$ of the
total mass of H$_2$O and Na is lost. Therefore, cumulative loss cannot
significantly modify Mercury's bulk mantle composition during the magma ocean
stage. Mercury's high core:mantle ratio and volatile-rich surface may instead
reflect chemical variations in its building blocks resulting from its
solar-proximal accretion environment.
