One of the most fundamental questions in the field of statistical mechanics is to explain the observed increase of a system's entropy in an irreversible process in terms of the underlying microscopic dynamics of the constituent particles. Recent work in dynamical systems theory (often called `chaos` theory) has allowed for considerable progress in this direction and for quantitative predictions to be made for both the quantities that describe the irreversible behavior of the system, such as transport coefficients, as well as the quantities that describe the system's chaotic behavior, such as Lyapunov exponents and dynamical `entropies`. The purpose of this research is to apply techniques of statistical mechanics to calculate both transport and dynamical quantities for systems of physical interest, and to relate them to each other and, in some cases, to the thermodynamic properties of the system. This will lead to a deeper understanding of the connections between the Second Law and microscopic dynamics. For quantum systems, this will also lead to further understanding of the behavior of some solid state devices of considerable current interest.
