  Transiting compact multi-planet systems provide many unique opportunities to
characterize the planets, including studies of size distributions, mean
densities, orbital dynamics, and atmospheric compositions. The relatively short
orbital periods in these systems ensure that events requiring specific orbital
locations of the planets (such as primary transit and secondary eclipse points)
occur with high frequency. The orbital motion and associated phase variations
of the planets provide a means to constrain the atmospheric compositions
through measurement of their albedos. Here we describe the expected phase
variations of the TRAPPIST-1 system and times of superior conjunction when the
summation of phase effects produce maximum amplitudes. We also describe the
infrared flux emitted by the TRAPPIST-1 planets and the influence on the
overall phase amplitudes. We further present the results from using the global
circulation model ROCKE-3D to model the atmospheres of TRAPPIST-1e and
TRAPPIST-1f assuming modern Earth and Archean atmospheric compositions. These
simulations are used to calculate predicted phase curves for both reflected
light and thermal emission components. We discuss the detectability of these
signatures and the future prospects for similar studies of phase variations for
relatively faint M stars.
