In this dissertation I present work on the development and application of molecular dynamics simulation methodologies for non-periodidic and non-equilibrium systems, culminating in the direct simulation of the interfacial thermal conductance of solvated, ligand-capped nanoparticles. Non-periodic geometries present problems for traditional affine scaling techniques in constant-pressure constant-temperature simulations. In particular, explicitly non-periodic systems or those containing materials with very different compressibilities are very difficult to simulate using exisiting methods. Our new method, the Langevin Hull, maintains a spherical boundary without the use of perturbative restraining or hard wall potentials. Velocity shearing and scaling reverse non-equilibrium molecular dynamics (VSS-RNEMD) for periodic systems is used to study the effect of ligand chain length and mixtures of chain lengths on the interfacial thermal conductance (G) of Au(111) interfaces protected by a monolayer of alkanethiolate ligands and solvated in hexane. There is no dependence on chain length for non-mixed layers, and a non-monotonic dependence of G on the fraction of long ligands included in a mixture of chain lengths. Proposed mechanisms for heat transfer rely on two competing effects: mobility of the interfacial solvent and vibrational orientational ordering between ligand and solvent molecules. Combination of the Langevin Hull non-periodic simulation method with existing VSS-RNEMD methodology yields a new non-periodic, non-equilibrium simulation method. The ability to impose kinetic energy and angular momentum fluxes in non-periodic geometries allows for the direct computation of transport properties in explicitly non-periodic systems. The interfacial thermal conductance and interfacial rotational friction are calculated for gold nanostructures solvated in a droplet of hexane, as well as the thermal conductivity of homogeneous metal and water clusters. Finally, the new non-periodic VSS-RNEMD is utilized to compute the interfacial thermal conductance of alkanethiolate ligand-protected gold nanoparticles solvated in a droplet of hexane. There is no discernible dependence of G on nanoparticle size, but a strong dependence on the length of the ligand alkane chain. The proposed heat transfer mechanisms are based on ligand chain flexibility, solvent penetration of the ligand layer, and ligand-induced restructuring of the nanoparticle surface.