- Abstract The analysis of dissipation and dephasing in driven mesoscopic devices requires a distinction between two notions of quantum irreversibility. One (" Loschmidt echo") is related to" time reversal", while the other is related to" driving reversal". In the latter context we define the time of maximum return (" compensation time") which generalizes the notion of" echo time". Non-perturbative features manifest themselves in the energy spreading process. This is demonstrated for the prototype random-matrix Wigner model, where the compensation time and the system response exhibit a non-universal scaling behavior.