Entropy Methods for the Boltzmann Equation: Lectures from a Special Semester at the Centre Émile Borel, Institut H. Poincaré, Paris, 2001 (Lecture Notes in Mathematics (1916))

Entropy and entropy production have recently become mathematical tools for kinetic and hydrodynamic limits, when deriving the macroscopic behaviour of systems from the interaction dynamics of their many microscopic elementary constituents at the atomic or molecular level. During a special semester on Hydrodynamic Limits at the Centre Émile Borel in Paris, 2001 two of the research courses were held by C. Villani and F. Rezakhanlou. Both illustrate the major role of entropy and entropy production in a mutual and complementary manner and have been written up and updated for joint publication. Villani describes the mathematical theory of convergence to equilibrium for the Boltzmann equation and its relation to various problems and fields, including information theory, logarithmic Sobolev inequalities and fluid mechanics. Rezakhanlou discusses four conjectures for the kinetic behaviour of the hard sphere models and formulates four stochastic variations of this model, also reviewing known results for these. "It is essential to force a U-turn in the way contemporary medicine approaches ill-health diseases. Early prevention of primary risk factors is a far more promising approach compared to late acute treatment of secondary risk factors in reducing the cost burden of Public Health, not mentioning the expected benefits of the former versus the latter approaches with regards to the Quality of Life. Wild-Type Food in Health Promotion and Disease Prevention: The Columbus Concept is one of the first books to focus on the role of omega-6/3 polyunsaturated fatty acids in unhealthy diets. The volume is divided into five sections. The first identifies the missing essential ratio of competing essential fatty acids in the human diet and relates them to the upsurge of modern chronic disease and associated health costs. The authors also explain the scientific basis of the Columbus Concept and the evidence supporting the rehabilitation of dietary/blood cholesterol. In the second section, authors discuss the essential ingredients in a daily diet that make blood vessels healthy and resistant. The third section introduces the functional part of the diet that brings about health benefits and healthy blood vessels. The fourth section details the health benefits of wild-type foods in various cultures. The final section investigates the possibility for novel sources for health promotion. Wild-Type Food in Health Promotion and Disease Prevention: The Columbus Concept presents a cutting-edge, in-depth investigation into new methods of health promotion."--Product description (www.bn.com) Fraydoun Rezakhanlou, Cédric Villani ; Editors: François Golse, Stefano Olla. Includes Bibliographical References And Index.