 This research in quantum thermodynamics focuses on heat transfer and rectification in nanoscales, developing a consistent approach for mesoscopic devices with continuous degrees of freedom that can handle weak to moderate non-linearities and external time-dependent fields, specifically analyzing one-dimensional and harmonic oscillator chains terminated by thermal reservoirs for rectification. This article was authored by T. Motts, M. Weidman, J. T. Stockberger, and others.