Violation of the fluctuation-response relation from a linear model of hair bundle oscillations

Spontaneous hair-bundle oscillations have been proposed to underlie the ear's active process, which amplifies acoustic signals, sharpens frequency selectivity, and broadens the dynamic range. Although this activity is critical for proper hearing, we know very little about its energetics and its nonequilibrium properties. Systems obey fluctuation-response relations, whose violation signals nonequilibrium conditions. Here we demonstrate the violation of the fluctuation-response relation of a linear model for hair bundle oscillations. Combining analytical results with experimental data, we estimate that an energy of at least 146 kBT is dissipated per oscillatory cycle, implying a power output of about 5 aW. Our model indicates that this dissipation attains a minimum at a certain characteristic frequency. For high frequencies, we derive a linear scaling behavior of this dissipated energy with the characteristic frequency.