Abstract:We present the derivation of the hydrodynamic limit under Eulerian scaling for a general class of one-dimensional interacting particle systems with two or more conservation laws. Following Yau's relative entropy method it turns out that in case of more than one conservation laws, in order that the system exhibit hydrodynamic behaviour, some particular identities reminiscent of Onsager's reciprocity relations must hold. We check validity of these identities whenever a stationary measure with product structure exists. It also follows that, as a general rule, the equilibrium thermodynamic entropy (as function of the densities of the conserved variables) is a globally convex Lax entropy of the hyperbolic systems of conservation laws arising as hydrodynamic limit. As concrete examples we also present a number of models modeling deposition (or domain growth) phenomena. The Onsager relations arising in the context of hydrodynamic limits under hyperbolic scaling seem to be novel.

**Paper:**- Available as PDF (304 Kbytes).
**Author(s):**- Balint Toth, <balint@math.bme.hu>
- Benedek Valko, <valko@math.bme.hu>
**Publishing information:**- Journal of Statistical Physics, vol. 112 (2003) pp. 497-521
**Comments:****Submitted by:**- <balint@math.bme.hu> December 15 2003.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | All Preprints | Preprint Server Homepage ]

Conservation Laws Preprint Server <conservation@math.ntnu.no> Last modified: Tue Dec 16 08:46:38 MET 2003