- For income distributions, city-size distributions and word
frequencies we observe skewed or long-tailed distributions of the
PAPETO-ZIPF type. In general - for properties of units belonging to the
same astrophysical, biological, ecological, urban, social, political,
economic or mechanical machinery system - we observe similar
regularities referred to as Pareto law, Zipfs law or rank-size law.
give a short historical overview over the discovery of these empirical
regularities. Then we review a variety of theoretical tentatives, none
of which can "explain" that similar regularities are observed in such
an incredible wide range of scientific research areas.
departing from a very specific model - describing tribo-vibro-acoustic
processes in machines - we propose a generalized theoretical framework
in terms of energy transformation with limited internal energy
dissipation capacity, which is applicable to all fields.
proposed model "unifies" a large variety of concepts and applies a
coherent terminology to fields, which have at first sight nothing in
common. For the observed life symptoms, theoretical predictions can be
compared with past and future empirical observations.
is most important is the model's inference power: from the observations
of a set of units at a given moment of life-time (a snapshot of the
system), one can predict the average behaviour of a single unit over
its entire life-time.
evolution, energy transformation, energy dissipation,
structure, information, autocatalysis, Pareto-Zipf or rank-size
vibration diagnostics, birth and death processes, symptom-life curve,
- *Bordalier Institute, 41270
Droué, France; *Poznan University of Technology, 60-965