  Ground-state cooling of mechanical motion by coupling to a driven optical
cavity has been demonstrated in various optomechanical systems. In our work, we
provide a so far missing thermodynamic performance analysis of optomechanical
sideband cooling in terms of a heat valve. As performance quantifiers, we
examine not only the lowest reachable effective temperature (phonon number) but
also the evacuated-heat flow as an equivalent to the cooling power of a
standard refrigerator, as well as appropriate thermodynamic efficiencies, which
all can be experimentally inferred from measurements of the cavity output light
field. Importantly, in addition to the standard optomechanical setup fed by
coherent light, we investigate two recent alternative setups for achieving
ground-state cooling: replacing the coherent laser drive by squeezed light or
using a cavity with a frequency-dependent (Fano) mirror. We study the dynamics
of these setups within and beyond the weak-coupling limit and give concrete
examples based on parameters of existing experimental systems. By applying our
thermodynamic framework, we gain detailed insights into these three different
optomechanical cooling setups, allowing a comprehensive understanding of the
thermodynamic mechanisms at play.
