The Behaviour of the Specific Entropy in the Hydrodynamic Scaling Limit for Ginzburg - Landau Model

#### E. Kosygina

2001, v.7, Issue 3, 383-417

ABSTRACT

The paper studies the behaviour of the specific entropy for Ginz-burg - Landau type models under the hydrodynamical scaling of time and space. It is shown that if the initial configurations possess a macroscopic profile, then for any fixed positive macroscopic time the specific microscopic entropy converges to the macroscopic entropy. The latter is defined in terms of the solution of the corresponding hydrodynamical equation, which is a non-linear diffusion equation. The above result is equivalent to the following statement: under the hydrodynamical scaling, for any positive macroscopic time the specific microscopic entropy relative to local Gibbs measures converges to zero.

Keywords: entropy,Ginzburg - Landau model,local Gibbs measures,hydrodynamical scaling limit,hydrodynamical equation