From Fermi-Pasta-Ulam Problem to Galaxies: The Quest for Relaxation

The major problem posed by the Fermi-Pasta-Ulam work was the relaxation (thermalization) of a many-body system. We review two approaches to this problem, the ergodic theory and Langevin (stochastic) equation ones, which have been applied for the description of statistical mechanics of stellar systems. Among the particular problems that we consider, are 1-dimensional long-range interacting systems and iterated maps and 3-dimensional N-body gravitating systems.