The Reversible Measures of Interacting Diffusion System with Plural Conservation Laws

#### H. Sakagawa

2001, v.7, Issue 2, 289-300

ABSTRACT

We consider the interacting diffusion system of Ginzburg - Landau type on a one-dimensional lattice, which has $N$ conservation laws when it is confined in a finite region. It is proved that the set of all reversible measures for such dynamics coincides with the set of canonical Gibbs measures associated with 2N conservation laws, namely the set of measures characterized by the DLR-equations conditioned by $2N$ quantities determined from inside data and also by external data for any finite subset of Z. This extends the previously known result for the dynamics with single conservation law (N=1) in the class of translation invariant measures.

Keywords: interacting diffusion system,conservation law,canonical Gibbsmeasure,quasi-invariance