A two-scale approach to the hydrodynamic limit, part II: local Gibbs behavior

This work is a follow-up on [GOVW]. In that previous work a two-scale approach was used to prove the logarithmic Sobolev inequality for a system of spins with fixed mean whose potential is a bounded perturbation of a Gaussian, and to derive an abstract theorem for the convergence to the hydrodynamic limit. This strategy was then successfully applied to Kawasaki dynamics. Here we shall use again this two-scale approach to show that the microscopic variable in such a model behaves according to a local Gibbs state. As a consequence, we shall prove the convergence of the microscopic entropy to the hydrodynamic entropy.Comment: 31 pages, 2nd version. The proof of Theorem 1.15 has been simplifie

Stabilization of the Witt group

Using an idea due to R.Thomason, we define a "homology theory" on the category of rings which satisfies excision, exactness, homotopy (in the algebraic sense) and periodicity of order 4. For regular noetherian rings, we find P. Balmer's higher Witt groups. For more general rings, this homology isomorphic to the KT-theory of J. Hornbostel, inspired by the work of B. Williams. For real or complex C*-algebras, we recover - up to 2 torsion - topological K-theory.Comment: 6 pages ; see also http://www.math.jussieu.fr/~karoubi