Non-equilibrium statistical mechanics: a growing frontier of “pure and applied” theoretical physics

Founded over a century ago, statistical mechanics for systems in thermal equilibrium has been so successful that, nowadays, it forms part of a typical physics core curriculum. On the other hand, most of “real life” phenomena occur under non-equilibrium conditions. Unfortunately, statistical mechanics for such systems is far from being well established. The goal of understanding complex collective behavior from simple microscopic rules (of evolution, say) remains elusive. As an example of the difficulties we face, consider predicting the existence of a tree from an appropriate collection of H,C,O,N,… atoms!
Over the last two decades, an increasing number of condensed matter theorists are devoting their efforts to this frontier. After a brief summary of the crucial differences between text-book equilibrium statistical mechanics and non-equilibrium statistical mechanics, I will give a bird’s-eye view of some key issues, ranging from the “fundamental” to (a small set of) the “applied.” The methods used also span a wide spectrum, from simple computer simulations to sophisticated field theoretic techniques. These will be illustrated in the context of a simple model for transport.