The question of how one can reconcile the second law of thermodynamics with microscopic time-reversal invariance goes back to the very beginning of statistical mechanics and the dispute between Boltzmann and Loschmidt. While the answer to this question is nowadays very well understood for classical systems, its quantum mechanical version has until recently hardly been explored. Besides its importance for the foundations of quantum statistical mechanics, the understanding of reversibility and irreversibility in quantum systems also plays an important role for example in spin echo experiments. In my talk I will give an overview of recent progress on this topic.
