While thermodynamics of physical systems in equilibrium is well-understood, non-equilibrium statistical mechanics still poses many open questions both in the classical and the quantum world. Hence, besides the development of deeper theoretical methods, the development of highly controlled physical many-body system in which to observe such non-equilibrium phenomena it is also of considerable interest. Trapped ion Coulomb crystals represent such a system. In this talk I will present recent result that we have obtained concerning the dynamics of structural phase transitions in ion Coulomb crystals [1,2,3] and novel approach to the underlying theory of the Kibble-Zurek effect . In a second part I will present a novel approach towards the spectroscopic examination of ion Coulomb crystals by means of multi-dimensional spectroscopy that we adapt and transfer from the field of nuclear magnetic resonance .
 S. Ulm, J. Roßnagel, G. Jacob, C. Degünther, S.T. Dawkins, U.G. Poschinger, R. Nigmatullin, A. Retzker, M.B. Plenio, F. Schmidt-Kaler and K. Singer. Observation of the Kibble-Zurek mechanism in ion crystals. Nature Comm. 4, 2290 (2013).
 K. Pyka, J. Keller, H. Partner, R. Nigmatullin, T. Burgermeister, D.M. Meier, K. Kuhlmann, A. Retzker, M.B. Plenio, W.H. Zurek, A. del Campo, T.E. Mehlstäubler. Causality and Defects as Relics of Symmetry Breaking in Ion Traps. Nature Comm. 4, 2291 (2013).
 H.L. Partner, T. Burgermeister, K. Pyka, J. Keller, T.E. Mehlstäubler, R. Nigmatullin, A. Retzker and M.B. Plenio. Dynamics of topological defects in ion Coulomb crystals. New J. Phys. 15, 103013 (2013).
 G. Nikoghosyan, R. Nigmatullin and M.B. Plenio. Universality in the Dynamics of Second-Order Phase Transitions. Phys. Rev. Lett. 116, 080601 (2016)
 A. Lemmer, C. Cormick, A. Schmiegelow, F. Schmidt-Kaler, and M.B. Plenio. Two-dimensional spectroscopy for the study of ion Coulomb crystals. Phys. Rev. Lett. 114, 073001 (2015)
Martin B Plenio is Alexander von Humboldt Professor and Director of the Institute of Theoretical Physics at Ulm University. He received his Diploma in 1992 and his PhD in 1994 from the Göttingen. From 1995 – 1997 he undertook postdoctoral research at Imperial College London. In 1998 he became permanent member academic staff and rose to Full Professor in 2003. In 2009 he was awarded an Alexander von Humboldt Professorship which he used to relocate to Ulm. His work covers a broad range of topics, including quantum information science, entanglement and coherence theory and quantum optics as well as the application of quantum technologies to sensing, medical imaging and the exploration of the role of quantum mechanics for biological function.. Published in nearly 300 papers, his work was awarded several prizes which include an Alexander von Humboldt Professorship, the Maxwell Medal and Prize, the Born Medal, and Prize of the Institute of Physics and the German Physical Society, as well as an ERC Synergy grant as well as funding for a €27Million Center for QuantumBioSciences.