  We estimate the canonical entropy of a quantum black hole by counting its
quasi-normal modes. We first show that the partition function of a classical
black hole, evaluated by counting the quasi-normal modes with a thermodyanmic
Boltzmann weight, leads to a small entropy of order unity due to the small
contribution from higher angular modes. We then discuss how this will be
modified when taking into account dissipation effects near the horizon due to
interaction with the quantum black hole microstates. The structure of
quasi-normal modes drastically changes, yielding a fundamental frequency of the
inverse of $t_{\rm echo} \sim$ log(Entropy)/Temperature. This is the time-scale
for reflection from the microstates (or the quantum time limit of silence,
followed by echoes), $\textit{independent of the strength of dissipation}$, and
is comparable to the scrambling time proposed by Sekino & Susskind. Setting the
dissipation constant to Planck time, we reproduce the Bekenstein-Hawking
entropy of $\sim$ (Horizon area)/(Planck area). This result suggests the
possibility of simulating black hole entropy in analog horizons realized in
condensed matter systems.
