(a) Power spectral density of transduced thermal motion, measured at room temperature (295 K). (b) Power spectral density of the group of peaks around the fundamental mechanical frequencies f1, f2 and around f1+f2, at room temperature (blue) and at 3 K (red). The orange arrows indicate the ratio between the maximum first- and second-order transduction (dashed lines). (c) Ratio between the 3 second-order peaks around f1+f2 and the peaks at the fundamental frequencies f1, f2 as a function of the relative cavity fluctuations δωr.m.s./κ. Device 1 is the same device presented in the other figures; device 2 is a similar device with different parameters from which more measurements are shown in Supplementary Note 2; room-temperature measurements from two recent publications are indicated with data points I (ref. 24) and II (ref. 36). The dashed line indicates the prediction from an analytical model with an order-by-order approximation, while the black data points connected with solid lines represent a calculation based on a numerically generated time trace to simulate thermal motion. (d) Expected band power at the fundamental frequency f as well as at 2f and 3f, as a function of the relative cavity fluctuations, normalized to the band power for f at δωr.m.s./κ=10−2. Solid, dashed, and dash-dotted lines follow the order-by-order approximation, while the coloured points are the outcome of our numerical model.