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.