Effects of breaking vibrational energy equipartition on measurements of temperature in macroscopic oscillators subject to heat flux

When the energy content of a resonant mode of a crystalline solid in thermodynamic equilibrium is directly measured, assuming that quantum effects can be neglected it coincides with temperature except for a proportionality factor. This is due to the principle of energy equipartition and the equilibrium hypothesis. However, most natural systems found in nature are not in thermodynamic equilibrium and thus the principle cannot be taken for granted. We measured the extent to which the low-frequency modes of vibration of a solid defy energy equipartition, in the presence of a steady state heat flux, even close to equilibrium. We found, experimentally and numerically, that the energy separately associated with low-frequency normal modes depends strongly on the heat flux, and decouples noticeably from temperature. A relative temperature difference of 4% across the object around room temperature suffices to excite two modes of a macroscopic oscillator, as if they were at equilibrium, separately, at temperatures about 20% and a factor of 3.5 higher. We interpret the result in terms of new flux-mediated correlations between modes in the nonequilibrium state which are absent at equilibrium.