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Entropies and Equilibria of ManyParticle Systems: An Essay on Recent Research

Summary: Entropies and Equilibria of Many­Particle
Systems: An Essay on Recent Research
J.A. Carrillo
L. Desvillettes
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


Source: Arnold, Anton - Institut für Analysis und Scientific Computing, Technische Universität Wien
Jüngel, Ansgar - Institut für Analysis und Scientific Computing, Technische Universität Wien
Pujo-Menjouet, Laurent - Institut Camille Jordan, Université Claude Bernard Lyon-I
Villani, Cédric - Institut Henri Poincaré


Collections: Biology and Medicine; Computer Technologies and Information Sciences; Mathematics