We use the thermodynamic global passivity methodology [1] to derive a set of inequalities on the second time derivatives of some observables. These inequalities are applicable to periodically driven or time-independent systems. As such, they can detect deviation from periodicity even far from steady state and when the periodic protocol is unknown. In the periodic version, the second time derivative is replaced by a discrete derivative which is easy to evaluate experimentally. We apply our result to quantum circuits and show that by running the circuit sequentially several times it is possible to detect some deviations of one cycle from the others. Crucially, in contrast to the second law, the presented thermodynamic-based inequalities are useful even when the initial state is pure, which is major advantage for practical application in quantum processors. We experimentally demonstrate our findings on the IBM quantum computer. We will also review a related experiment we recently carried out on the IBM platform [2].

[1] R. Uzdin and S. Rahav, “Global passivity”, Phys. Rev. X 8, 021064 (2018)
[2] I. Henao, N. Katz, and R. Uzdin, “Experimental detection of microscopic environments using thermodynamic observables”, 
 arXiv:1908.08968