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Life Symptoms: the Behaviour of Open Systems with Limited Energy Dissipation Capacity and Evolution*

Peter Winiwarter* and Czeslaw Cempel**

Abstract - 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.

We 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.

Finally, 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.

The 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.

What 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.

Keywords-Self-organization, evolution, energy transformation, energy dissipation,

internal structure, information, autocatalysis, Pareto-Zipf or rank-size distributions,

machine vibration diagnostics, birth and death processes, symptom-life curve, residual life-time.

Address -   *Bordalier Institute, 41270 Droué, France; *Poznan University of Technology, 60-965 Poznan, Poland.