From entropy to echoes: Counting the quasi-normal modes and the quantum limit of silence

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