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 granted. We measured the extent to which the low-frequency modes of vibration of a solid can defy energy equipartition, in 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 strongly depends on the heat flux, and decouples sensibly from temperature. A 4% in the relative temperature difference across the object around room temperature suffices to excite two modes of a macroscopic oscillator, as if they were at equilibrium, respectively, at temperatures about 20% and a factor 3.5 higher. We interpret the result in terms of new fluxmediated correlations between modes in the nonequilibrium state, which are absent at equilibrium.

We study experimentally, numerically, and theoretically the elastic response of mechanical resonators along which the temperature is not uniform, as a consequence of the onset of steady-state thermal gradients. Two experimental setups and designs are employed, both using low-loss materials. In both cases, we monitor the resonance frequencies of specific modes of vibration, as they vary along with variations of temperatures and of temperature differences. In one case, we consider the first longitudinal mode of vibration of an aluminum alloy resonator; in the other case, we consider the antisymmetric torsion modes of a silicon resonator. By defining the average temperature as the volume-weighted mean of the temperatures of the respective elastic sections, we find out that the elastic response of an object depends solely on it, regardless of whether a thermal gradient exists and, up to 10% imbalance, regardless of its magnitude. The numerical model employs a chain of anharmonic oscillators, with first- and second-neighbor interactions and temperature profiles satisfying Fourier's Law to a good degree. Its analysis confirms, for the most part, the experimental findings and it is explained theoretically from a statistical mechanics perspective with a loose notion of local equilibrium.

No abstract

No abstract