  The Boson peak is believed to be the key to the fundamental understanding of
the anomalous thermodynamic properties of glasses, notably the anomalous peak
in the heat capacity at low temperatures; it is believed to be due to an excess
of low frequency vibrational modes and a manifestation of the structural
disorder in these systems. We study the thermodynamics and vibrational dynamics
of colloidal glasses and (defected) crystals. The experimental determination of
the vibrational density of states allows us to directly observe the Boson peak
as a strong enhancement of low frequency modes. Using a novel method [Zargar et
al., Phys. Rev. Lett. 110, 258301 (2013)] to determine the free energy, we also
determine the entropy and the specific heat experimentally. It follows that the
emergence of the Boson peak and high values of the specific heat are directly
related and are specific to the glass: for a very defected crystal with a
disorder that is only slightly smaller than for the glass, both the
low-frequency density of states and the specific heat are significantly smaller
than in the glass.
