  JWST observations of the 7-planet TRAPPIST-1 system will provide an excellent
opportunity to test outcomes of stellar-driven evolution of terrestrial
planetary atmospheres, including atmospheric escape, ocean loss and abiotic
oxygen production. While most previous studies use a single luminosity
evolution for the host star, we incorporate observational uncertainties in
stellar mass, luminosity evolution, system age, and planetary parameters to
statistically explore the plausible range of planetary atmospheric escape
outcomes. We present probabilistic distributions of total water loss and oxygen
production as a function of initial water content, for planets with initially
pure water atmospheres and no interior-atmosphere exchange. We find that the
interior planets are desiccated for initial water contents below 50 Earth
oceans. For TRAPPIST-1e, f, g, and h, we report maximum water loss ranges of
8.0$^{+1.3}_{-0.9}$, 4.8$^{+0.6}_{-0.4}$, 3.4$^{+0.3}_{-0.3}$, and
0.8$^{+0.2}_{-0.1}$ Earth oceans, respectively, with corresponding maximum
oxygen retention of 1290$^{+75}_{-75}$, 800$^{+40}_{-40}$, 560$^{+30}_{-25}$,
and 90$^{+10}_{-10}$ bars. We explore statistical constraints on initial water
content imposed by current water content, which could inform evolutionary
history and planet formation. If TRAPPIST-1b is airless while TRAPPIST-1c
possesses a tenuous oxygen atmosphere, as initial JWST observations suggest,
then our models predict an initial surface water content of 8.2$^{+1.5}_{-1.0}$
Earth oceans for these worlds, leading to the outer planets retaining $>$1.5
Earth oceans after entering the habitable zone. Even if TRAPPIST-1c is airless,
surface water on the outer planets would not be precluded.
