Recurrence in Physical and Social Systems.
Author: Wolfgang Weidlich
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's 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 quasi-periodic 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), sociology (group
dynamics), and economics (demand dynamics).
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