Nonequilibrium Dynamics for Reversible Lattice Gases

Abstract

We have reached a main goal of our undertaking: The study of the dynamics for configurations whose density varies slowly on the scale of the lattice. As before we consider a reversible lattice gas. Its rates satisfy the condition of detailed balance, cf. Eq. (1.31). (We consider here only the high temperature situation and assume the potential for H to be sufficiently small such that the exponential mixing (1.39) holds over the full range of densities, cf. Theorem 1.8 for an explicit condition.) It is natural to take thermal equilibrium as our starting point. The distribution of particles in the box Λ ⊂ ℤ^d with uniform density is then given by

$$ \frac{1}{Z}\exp \left[ { - H + \lambda \sum\limits_{{x \in \wedge }} {\eta \left( x \right)} } \right]. $$

(3.1)