How Close Is the Ear to the Thermal Limit? An Energy Recount at the Threshold of Hearing

We recount the acoustic energy delivered to the human eardrum at 0 dB SPL near 3.5 kHz. Threshold intensity is 9.69e-13 W/m2 and intercepted power is 5.33e-17 W; over 0.2 s the energy is 1.07e-17 J, 2489 times kT at 310 K (34.0 dB), but per acoustic cycle it is only 3.6 times kT. The ear operates within a small factor of the thermal limit per cycle, but not at it, with middle-ear gain (~27 dB) and cochlear amplification (40-60 dB) completing the bookkeeping.