Inference of Time-Reversal Asymmetry from Time Series in a Piezoelectric Energy Harvester

We consider the problem of assessing the non-equilibrium behavior of a system from the study of time series. In particular, we analyze experimental data from a piezoelectric energy harvester driven by broadband random vibrations where the extracted power and the relative tip displacement can be simultaneously measured. We compute autocorrelation and cross-correlation functions of these quantities in order to investigate the system properties under time reversal. We support our findings with numerical simulations of a linear underdamped Langevin equation, which very well describes the dynamics and fluctuations of the energy harvester. Our study shows that, due to the linearity of the system, from the analysis of a single variable, it is not possible to evidence the non-equilibrium nature of the dynamics. On the other hand, when cross-correlations are considered, the irreversible nature of the dynamics can be revealed.