Statistical mechanical theory of transport and relaxation processes in interacting lattice systems

The dynamics of lattice systems are described by the irreversible Markovian master equation that is used to calculate microscopic particle and energy fluxes. After reduction of the description the deviations of particle and energy densities from their equilibrium values obey a system of non-Markovian equations that allow one to deduce microscopic expressions for different transport coefficients. All the expressions consist of two parts: one proportional to a static correlation function and the other to the time integral of a time correlation function. The relevant or quasi-equilibrium distribution contributes significantly to transport coefficients contrary to systems obeying the reversible, e.g. Hamiltonian dynamics. At some conditions the memory effects can be disregarded. Then the transport coefficients are represented by lattice gas equilibrium characteristics that are calculated within the self-consistent diagram approximation. Transport coefficients depend on thermodynamic conditions (concentration and temperature) leading to strongly non-linear transport equations.