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Summary: Entropies and Equilibria of ManyParticle
Systems: An Essay on Recent Research
A.Arnold
J.A. Carrillo
L. Desvillettes
J.Dolbeault§
A. J¨ungel¶
C. Lederman P.A. Markowich
G. Toscani
C. Villani
1 Motivation and Applications
In the fast moving development of new technologies, ranging from microelectronics to space
crafts, applied mathematics plays a substantial role in two fundamental steps of the realiza-
tion process: modeling and numerical simulation. These two issues are closely connected,
and vital to continuously improve the physical description of the relevant phenomena. In
many novel applications the modeling involves the knowledge of the behavior of systems
composed of a large number of interacting particles: electrons in micro-devices, ions in the
plasma of fusion reactors, atoms in a BoseEinstein condensate, gas flowing over the wings
of aircrafts, etc. One of the main features of such systems is their tendency (if left alone) to
converge to an equilibrium configuration as time becomes large (usually this time is rather
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