  Amongst the class of supergravity solutions found by Lin, Lunin and
Maldacena, we consider pure and mixed state configurations generated by phase
space densities in the dual fermionic picture. A one-to-one map is constructed
between the phase space densities and piecewise monotonic curves, which
generalize the Young diagrams corresponding to pure states. Within the
fermionic phase space picture, a microscopic formula for the entropy of mixed
states is proposed. Considering thermal ensembles, agreement is found between
the thermodynamic and the proposed microscopic entropies. Furthermore, we study
fluctuations in thermodynamic ensembles for the superstar and compare the
entropy of these ensembles with the area of stretched horizons predicted by the
mean fluctuation size.
