Projective measurement is a commonly used assumption in quantum mechanics. However, advances in quantum measurement techniques allow for partial measurements, which accurately estimate state information while keeping the wavefunction intact. In this dissertation, we employ partial measurements to study two phenomena. First, we investigate an uncertainty relation -- in the style of Heisenberg's 1929 thought experiment -- which includes partial measurements in addition to projective measurements. We find that a weak partial measurement can decrease the uncertainty between two incompatible (non-commuting) observables. In the second study, we investigate the foundation of irreversible dynamics resulting from partial measurements. We do so by comparing the forward and time-reversed probabilities of measurement outcomes resulting from post-selected feedback protocols with both causal and reversed-causal order. We find that the statistics of partial measurements produce entropy in accordance with generalized second laws of thermodynamics. We perform these experiments using superconducting qubits. This dissertation also describes the fabrication process for these devices and details a novel fabrication technique that allows fast, single-step lithography of Josephson-junction superconducting circuits. The technique simplifies processing by utilizing a direct-write photolithography system, in contrast to traditional electron-beam lithography. Despite their large lithographic area, Josephson junctions made with this method have low critical currents and high coherence times.