Chaos theoryChaos theory is an interdisciplinary area of scientific study and branch of mathematics focused on underlying patterns and deterministic laws of dynamical systems that are highly sensitive to initial conditions, and were once thought to have completely random states of disorder and irregularities. Chaos theory states that within the apparent randomness of chaotic complex systems, there are underlying patterns, interconnection, constant feedback loops, repetition, self-similarity, fractals, and self-organization.
Dissipative systemA dissipative system is a thermodynamically open system which is operating out of, and often far from, thermodynamic equilibrium in an environment with which it exchanges energy and matter. A tornado may be thought of as a dissipative system. Dissipative systems stand in contrast to conservative systems. A dissipative structure is a dissipative system that has a dynamical regime that is in some sense in a reproducible steady state. This reproducible steady state may be reached by natural evolution of the system, by artifice, or by a combination of these two.
Paris CommuneThe Paris Commune (Commune de Paris, kɔ.myn də pa.ʁi) was a French revolutionary government that seized power in Paris from 18 March to 28 May 1871. During the Franco-Prussian War of 1870–71, the French National Guard had defended Paris, and working-class radicalism grew among its soldiers. Following the establishment of the Third Republic in September 1870 (under French chief executive Adolphe Thiers from February 1871) and the complete defeat of the French Army by the Germans by March 1871, soldiers of the National Guard seized control of the city on March 18.
Communes of FranceThe commune (kɔmyn) is a level of administrative division in the French Republic. French communes are analogous to civil townships and incorporated municipalities in the United States and Canada, Gemeinden in Germany, comuni in Italy, or municipios in Spain. The UK equivalent are civil parishes. Communes are based on historical geographic communities or villages and are vested with significant powers to manage the populations and land of the geographic area covered. The communes are the fourth-level administrative divisions of France.
Conservative systemIn mathematics, a conservative system is a dynamical system which stands in contrast to a dissipative system. Roughly speaking, such systems have no friction or other mechanism to dissipate the dynamics, and thus, their phase space does not shrink over time. Precisely speaking, they are those dynamical systems that have a null wandering set: under time evolution, no portion of the phase space ever "wanders away", never to be returned to or revisited. Alternately, conservative systems are those to which the Poincaré recurrence theorem applies.
