An introduction to phase transitions in stochastic dynamical systems

Abstract

We give an introduction to phase transitions in the steady states of systems that evolve stochastically with equilibrium and nonequilibrium dynamics, the latter defined as those that do not possess a time-reversal symmetry. We try as much as possible to discuss both cases within the same conceptual framework, focussing on dynamically attractive `peaks' in state space. A quantitative characterisation of these peaks leads to expressions for the partition function and free energy that extend from equilibrium steady states to their nonequilibrium counterparts. We show that for certain classes of nonequilibrium systems that have been exactly solved, these expressions provide precise predictions of their macroscopic phase behaviour.Comment: Pedagogical talk contributed to the "Ageing and the Glass Transition" Summer School, Luxembourg, September 2005. 12 pages, 8 figures, uses the IOP 'jpconf' document clas