Achieving a precise understanding of galaxy formation in a cosmological context is one of the great challenges in theoretical astrophysics, due to the vast range of spatial scales involved in the relevant physical processes. Observations in the millimeter bands, particularly those using the cosmic microwave background (CMB) radiation as a backlight, provide a unique probe of the thermodynamics of these processes, with the capability to directly measure the density, pressure, and temperature of ionized gas. Moreover, these observations have uniquely high sensitivity into the outskirts of the halos of galaxies and clusters, including systems at high redshift. In the next decade, the combination of large spectroscopic and photometric optical galaxy surveys and wide-field, low-noise CMB surveys will transform our understanding of galaxy formation via these probes.
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