Dynamical-system models of transport: chaos characteristics, the macroscopic limit, and irreversibility

The escape-rate formalism and the thermostating algorithm describe relaxation towards a decaying state with absorbing boundaries and a steady state of periodic systems, respectively. It has been shown that the key features of the transport properties of both approaches, if modeled by low-dimensional dynamical systems, can conveniently be described in the framework of multibaker maps. In the present paper we discuss in detail the steps required to reach a meaningful macroscopic limit. The limit involves a sequence of coarser and coarser descriptions (projections) until one reaches the level of irreversible macroscopic advection–diffusion equations. The influence of boundary conditions is studied in detail. Only a few of the chaos characteristics possess a meaningful macroscopic limit, but none of these is sufficient to determine the entropy production in a general non-equilibrium state.