Entropy methods in hydrodynamic scaling. (English) Zbl 0791.60098

Cercignani, Carlo (ed.) et al., Nonequilibrium problems in many-particle systems. Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini, Italy, June 15-27, 1992. Berlin: Springer-Verlag. Lect. Notes Math. 1551, 112-145 (1993).
This review article is motivated by a simple example of the free particles of the lattice points arranged uniformly on the circle (Section 1) and then complicated by the Ginzburg-Landau type interaction (Section 2). Large deviations and the method of relative entropy is the subject of the Sections 3 and 4. In Section 5 the problem of transition from the Hamiltonian system to the Euler’s equations is considered. In the concluding Section 6 some extensions of the previous models are examined. They are the interacting Brownian motions on the circle and a modified Ginzburg-Landau model.
For the entire collection see [Zbl 0777.00027].


60K35 Interacting random processes; statistical mechanics type models; percolation theory
60F10 Large deviations