  Proxima Centauri b provides an unprecedented opportunity to understand the
evolution and nature of terrestrial planets orbiting M dwarfs. Although Proxima
Cen b orbits within its star's habitable zone, multiple plausible evolutionary
paths could have generated different environments that may or may not be
habitable. Here we use 1D coupled climate-photochemical models to generate
self-consistent atmospheres for evolutionary scenarios predicted in our
companion paper (Barnes et al., 2016). These include high-O2, high-CO2, and
more Earth-like atmospheres, with either oxidizing or reducing compositions. We
show that these modeled environments can be habitable or uninhabitable at
Proxima Cen b's position in the habitable zone. We use radiative transfer
models to generate synthetic spectra and thermal phase curves for these
simulated environments, and instrument models to explore our ability to
discriminate between possible planetary states. These results are applicable
not only to Proxima Cen b, but to other terrestrial planets orbiting M dwarfs.
Thermal phase curves may provide the first constraint on the existence of an
atmosphere, and JWST observations longward of 7 microns could characterize
atmospheric heat transport and molecular composition. Detection of ocean glint
is unlikely with JWST, but may be within the reach of larger aperture
telescopes. Direct imaging spectra may detect O4, which is diagnostic of
massive water loss and O2 retention, rather than a photosynthesis. Similarly,
strong CO2 and CO bands at wavelengths shortward of 2.5 {\mu}m would indicate a
CO2-dominated atmosphere. If the planet is habitable and volatile-rich, direct
imaging will be the best means of detecting habitability. Earth-like planets
with microbial biospheres may be identified by the presence of CH4 and either
photosynthetically produced O2 or a hydrocarbon haze layer.
