One of the fundamental concepts in statistical mechanics is the notion of ergodicity, which is closely related to the lack of memory of a system. In quantum mechanics, it is observed that the interactions redistribute the available
energy and enable thermalization . Under some conditions, however, an external drive can inhibit ergodicity [3–5]. In this case, the system looses the ability to explore all the available states [6–10] and keeps memory of the initial state. In this talk, I will discuss a model where ergodic behavior is broken due to integrability. The reduced dynamics of such as system is given by a time-local master equation with time-periodic rates. Due to the time-periodicity of the master equation, the dynamical map is divisible at discrete times, which is referred to as Floquet stroboscopic divisibility . I will illustrate general theory by studying an oscillator coupled to both non-Markovian and Markovian baths. In this example, if one prepares the system in a cat state, the environment induces stroboscopic revivals of the cat after its death. Our theory may have profound implications in entropy production in non-equilibrium systems.
 M. Srednicki, Phys. Rev. E 50, 888 (1994).
 A. Lazarides, A. Das, and R. Moessner, Phys. Rev. Lett. 115, 030402 (2015).
 S. Restrepo, J. Cerrillo, V. M. Bastidas, D. G. Angelakis, and T. Brandes, Phys. Rev. Lett. 117, 250401 (2016).
 A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).
 V. M. Bastidas, B. Renoust, Kae Nemoto, W. J. Munro, arXiv:1807.00080 (2018).
 D. Basko, I. Aleiner, B. Altshuler, Ann. Phys. 321, 1126 (2006).
 R. Nandkishore, D. A. Huse, Annu. Rev. Condens. Matter Phys. 6, 15 (2015).
 E. Altman, R. Vosk, Annu. Rev. Condens. Matter Phys. 6, 383 (2015).
 M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, I. Bloch, Science
349, 842 (2015).
 P. Roushan, C. Neill, J. Tangpanitanon, V. M. Bastidas, A. Megrant, R. Barends, Y. Chen, Z. Chen, B. Chiaro, A.
Dunsworth, A. Fowler, B. Foxen, M. Giustina, E. Jeffrey, J. Kelly, E. Lucero, J. Mutus,1 M. Neeley, C. Quintana, D. Sank,
A. Vainsencher, J. Wenner, T. White, H. Neven, D. G. Angelakis, J. Martinis, Science 358, 1175 (2017).
 V. M. Bastidas, T. H. Kyaw, J. Tangpanitanon, G. Romero, L.-C. Kwek, D. G. Angelakis, New J. Phys. 20, 093004 (2018).