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Abstract  

Statistics: Order-disorder problems in many-particle statistics may be solved by the Lagrange principle: L=TlogP+E→maximum! L is the Lagrange function, logP the entropy and E a special condition of order for a system of interacting objects. T is an ordering parameter: for low values of T order (E), for high values of T, disorder or chaos (logP) will be at maximum. Natural sciences: The Lagrange principle corresponds to Gibbs energy. The cohesive energy E leads to the three structures of matter: the well-ordered solid and the disordered liquid and gas. In binary systems, L leads to phase diagrams and solubility or segregation of materials. Society: L corresponds to common happiness, which has to be at maximum for a stable society. Emotions E: sympathy, apathy, antipathy lead to three social structures: the well-ordered hierarchy and the disordered democracy and the global state. In binary societies(women-men, black-non-black, Catholics-non-Catholics) intermarriage diagrams correspond to phase diagrams and show the state of integration or segregation, peace or war of the society. Economics: L corresponds to common benefit, which has to be at maximum for a stable economy, and leads to a (capitalistic) Boltzmann distribution of property E. Economic cycles of production and trade correspond to Carnot cycles of a gas in engineering sciences: a motor works at two different temperatures, economic cycles will tend to produce two different standards of living, rich and poor, or first and the third world. History: Industrial development corresponds to a heating curve of alloys: the growing productivity has melted away the inflexible structure of monarchies, and has (slowly) transformed Europe into a flexible democratic structure. The French Revolution may be regarded as (first-order) phase transition. Recent takeovers of very big companies show a trend to global activity, free from national ties.

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