The Cochlear Amplifier Power Budget: Mechanical Power per Outer Hair Cell, Its Margin over the Thermal Floor, and Its Cost against Metabolism

How much mechanical power does the cochlear amplifier deliver, and how close does it run to its own limits? Treating one resonant basilar-membrane segment at 2,000 Hz as a damped oscillator, the dissipated (hence amplifier-supplied) power is 3.125e-17 W per segment at threshold, 7.814e-14 W at 60 dB SPL and 4.254e-13 W at 80 dB SPL. Per active outer hair cell the output is 9.116e-18 W at threshold, 2.272e-14 W at 60 dB SPL and 1.237e-13 W at 80 dB SPL; a single tone's active region (150 segments, about 514 cells) receives 4.688e-15 W at threshold and 1.168e-11 W at 60 dB SPL, and all 12,000 outer hair cells at the 60 dB rate would deliver 2.726e-10 W. Against the thermal floor the threshold mode energy is 3.49 kT and the threshold displacement is 2.64 times the thermal rms displacement. Against metabolism the output is 0.284 per cent of a cell's electrical throughput at 60 dB SPL, rising to 1.55 per cent at 80 dB SPL. A force-times-velocity cross-check agrees within a factor of 2.41. All numbers are produced by the deposited compute.py. AI use is disclosed: drafting and computation assistance was provided by Dave, an AI system built and operated under the author's direction. The author, William Alexander Aldred, directed the work and is sole author of record.