“The importance of knowledge consists not only in its direct practical utility but also in the fact the it promotes a widely contemplative habit of mind; on this ground, utility is to be found in much of the knowledge that is nowadays labelled ‘useless’. ” Bertrand Russel, In Praise of Idleness, London (1935) “Why are scientists in so many cases so deeply interested in their work ? Is it merely because it is useful ? It is only necessary to talk to such scientists to discover that the utilitarian possibilities of their work are generally of secondary interest to them. Something else is primary. ” David Bohm, On creativity, Abingdon (1996) In this volume, the dynamical critical behaviour of many-body systems far from equilibrium is discussed. Therefore, the intrinsic properties of the - namics itself, rather than those of the stationary state, are in the focus of 1 interest. Characteristically, far-from-equilibrium systems often display - namical scaling, even if the stationary state is very far from being critical. A 1 As an example of a non-equilibrium phase transition, with striking practical c- sequences, consider the allotropic change of metallic ?-tin to brittle ?-tin. At o equilibrium, the gray ?-Sn becomes more stable than the silvery ?-Sn at 13. 2 C. Kinetically, the transition between these two solid forms of tin is rather slow at higher temperatures. It starts from small islands of ?-Sn, the growth of which proceeds through an auto-catalytic reaction.

This booklet is devoted to the thermodynamic and kinetic description of first-order phase transitions. In general, the matter of the world exists in different phases. Normally phase ctlanges take place in ther­ modynamic equilibrium, which will be considered here. Typically,the system is rapidly quenched from a one-phase thermal equilibrium state to a nonequilibrium situation. During the so-ca lIed equilibrium phase transformation process the quenched supersaturated system evolves from the nonequilibrium state to an equilibrium one which consists of two coexisting phases. In aseries of books on phase transitions and critical phenomena (DDMB, GREEN, lEBDWITZ, 1972 - 19B3) an immense amount of material to different aspects of ttlis topic is summarized. The other type of phase transitions takes place in systems far from equilibrium. Due to 'the nonequi1ibrium boundary conditions and the flu­ xes from the environment into the system the final state of this so­ called nonequilibrium phase transition is a stable nonequilibrium si­ tuation. Such interesting processes (e. g. pattern formation, multista­ bi1ity) do not appear only in physics but also in chemistry, meteorolo­ gy, biology and many areas of engineering. Concerning questions in this context we recommend the reader to the monographs by HAKEN (197B), and EBElING, FEISTEl (1982). An overview of the problems of recent interest in this field is given in the Proceedings of the Third International Conference on Irreversible Processes and Dissipative Structures, edited by EBElING and Ul8RICHT (1986).

In this book, the equilibrium and nonequilibrium properties of continuous phase transitions are studied in various systems, with a special emphasis on understanding how well-established universal traits at equilibrium may be extended into the dynamic realm, going beyond the paradigmatic Kibble–Zurek mechanism of defect formation. This book reports on the existence of a quantum phase transition in a system comprising just a single spin and a bosonic mode (the quantum Rabi model). Though critical phenomena are inherent to many-body physics, the author demonstrates that this small and ostensibly simple system allows us to explore the rich phenomenology of phase transitions, both in- and out-of-equilibrium. Moreover, the universal traits of this quantum phase transition may be realized in a single trapped-ion experiment, thus avoiding the need to scale up the number of constituents. In this system, the phase transition takes place in a suitable limit of system parameters rather than in the conventional thermodynamic limit – a novel notion that the author and his collaborators have dubbed the finite-component system phase transition. As such, the results gathered in this book will open promising new avenues in our understanding and exploration of quantum critical phenomena.

This book describes two main classes of non-equilibrium phase-transitions: static and dynamics of transitions into an absorbing state, and dynamical scaling in far-from-equilibrium relaxation behavior and ageing.