  A critically important process affecting the climate evolution and potential
habitability of an exoplanet is atmospheric escape, in which high-energy
radiation from a star drives the escape of hydrogen atoms and other light
elements from a planet's atmosphere. L 98-59 is a benchmark system for studying
such atmospheric processes, with three transiting terrestrial-size planets
receiving Venus-like instellations (4-25 S$_\oplus$) from their M3 host star.
We use the VPLanet model to simulate the evolution of the L 98-59 system and
the atmospheric escape of its inner three small planets, given different
assumed initial water quantities. We find that, regardless of their initial
water content, all three planets accumulate significant quantities of oxygen
due to efficient water photolysis and hydrogen loss. All three planets also
receive enough XUV flux to drive rapid water loss, which considerably affects
their developing climates and atmospheres. Even in scenarios of low initial
water content, our results suggest that the James Webb Space Telescope (JWST)
will be sensitive to observations of retained oxygen on the L 98-59 planets in
its future scheduled observations, with planets b and c being the most likely
targets to possess an extended atmosphere. Our results constrain the
atmospheric evolution of these small rocky planets, and they provide context
for current and future observations of the L 98-59 system to generalize our
understanding of multi-terrestrial planet systems.
