Yukio Nagahata

The Gradient Condition for One-Dimensional Symmetric Exclusion Processes

For every Gibbs measure on the one dimensional lattice Z with translation-invariant potential of finite range, an exchange rate for one-dimensional lattice gas which satisfy both the detailed balance condition relative to the Gibbs measure and the gradient condition is constructed.

Fluctuation Dissipation Equation for Lattice Gas with Energy

In this paper we introduce a “lattice gas with energy,” and obtain the “fluctuation dissipation equation” for it. The system has two conserved quantities, the number of particles and the total energy. Once the “fluctuation dissipation equation” is established, the hydrodynamic limit is easily deduced from it by using the methods found in ref. 1 for this model.