Recurrence in Physical and Social Systems

The problem of the relation between recurrence and irreversibility is an old and universal one: it has been discussed by philosophers, physicists, historians, and social scientists. After briefly mentioning philosophical formulations of the problem, the controversy, being deeply inherent in the notions of Statistical Physics, is discussed in terms of Poincare’ recurrence theorem versus irreversible equations such as the Boltzmann equation. The conclusion is that the neglection of certain correlations, i.e., an approximation, leads from recurrence to irreversibility. Thereupon the inverse problem is considered, in which manner recurrent, in particular periodic or quasiperiodic sub-processes can appear to be embedded in a globally irreversible process. Some approaches how to trace and recognize embedded recurrent (and even periodic) sub-processes are discussed. Finally, selected examples of model-based (quasi-) periodic processes in social systems are presented. They belong to the sectors demography (migration) and sociology (group dynamics).