| The objective of this study is to explore the application of methods from non-equilibrium statistical mechanics to the study of granular fluids. This exploration is carried out in the specific context of obtaining a hydrodynamic description for these fluids that is based unambiguously on an underlying microscopic theory. A particular model of a granular fluid amenable for theoretical study, namely inelastic hard spheres, is considered. The isolated homogeneous system is studied and the associated ensemble characterized. Then, small perturbations away from this reference ensemble are considered with the aim of isolating the hydrodynamic response of the system and hence obtaining microscopic expressions for the various hydrodynamic transport coefficients. The primary outcomes of this project are exact Green-Kubo and Helfand forms for all the hydrodynamic transport coefficients. These expressions are a first of their kind in that they do not have any a priori limitations on the domain of their validity, unlike those obtained from kinetic theory that exist in the literature so far. These exact forms are a well defined starting point for further analytic and numerical analysis in order to obtain useful insight into the nature of transport in this fluid. First steps in this direction are taken by comparing the exact forms to their counterparts for normal fluids and by developing the kinetic theory of time correlation functions that relate the results in the present work with those already given in the literature. |
