Investigations of $p$+Pb Collisions at Perturbative and Non-Perturbative QCD Scales

High energy nuclear collisions manifest a variety of interesting phenomena over a broad range of energy scales. Many of these phenomena are related to the formation of a hot and dense state of deconfined quarks and gluons known as the quark gluon plasma (QGP). Chief among these are the observed near inviscid hydrodynamic expansion of the QGP, as measured through azimuthal anisotropy coefficients of low-$p_\mathrm{T}$ final state hadrons $v_\mathrm{n}$, and the loss of energy of high-$p_\mathrm{T}$ color charges as they traverse the QGP which is observed as a quenching of strongly-interacting final state objects like jets. Observations of these phenomena in Au+Au and Pb+Pb collisions at RHIC and the LHC provide compelling evidence of QGP formation. Small collision systems, like $p$+Pb, also show evidence for the creation droplets of QGP through the observation of anisotropic flow; however, measurements of high-$p_\mathrm{T}$ jet and particle spectra show no signs of the energy loss observed in large collision systems. Thus, small systems are an ideal venue to explore the relationship between high- and low-$p_\mathrm{T}$ QGP phenomena. Furthermore, the low ambient energy of $p$+Pb compared to A+A collisions allow for the precise determination of perturbative process rates which can be used to understand the nuclear modification of nucleon parton densities. This dissertation explores 165~nb$^{-1}$ of 8.16~\TeV{} $p$+Pb data collected in 2016 with the ATLAS detector at the LHC through the exposition of two measurements. The cross section and nuclear modification factor for prompt, isolated photons are studied over a broad range of transverse energies and rapidities. These results are compared to predictions from perturbative QCD calculations and a model of initial state energy loss. Additionally, the charged hadron azimuthal anisotropy coefficients, $v_\mathrm{2}$ and $v_\mathrm{3}$, are measured via two-particle correlations as a function of particle $p_\mathrm{T}$ and event centrality. Results are shown from minimum bias events and events selected because of the presence of a high-$p_\mathrm{T}$ jet. The elliptic flow coefficient is observed to be non-zero for $0.5<p_\mathrm{T}<50$~\GeV. These results are discussed in the context of hydrodynamic and energy loss models.