Corwin, EricTrevelyan, Alexander2018-10-312018-10-312018-10-31https://hdl.handle.net/1794/23915The ability to probe many-particle systems on a microscopic level has revolutionized the way we do statistical physics. As computational capabilities continue to grow exponentially, larger and more complex systems come within reach of microscopic analysis. In the field of network growth, the classical model has given way to competitive processes, in which networks are guided by some criteria at every step of their formation. We develop and analyze a new competitive growth process that permits intervention on growing networks using only local properties of the network when evaluating how to add new connections. We establish the critical behavior of this new method and explore potential uses in guiding the development of real-world networks. The classical system of electrons diffusing within a conductor similarly permits a microscopic analysis where, to date, studies of the macroscopic properties have dominated the literature. In order to extend our understanding of the theory that governs this diffusion—the fluctuation-dissipation theorem—we construct a physical model of the Johnson-Nyquist system of electrons embedded in the bulk of a conductor. Constructing the model involves deriving how the motion of each individual electron comes about via scattering processes in the conductor, then connecting this collective motion to the macroscopic observables of voltage and current that define Johnson-Nyquist noise. Once the equilibrium properties have been fully realized, an external perturbation can be applied in order to probe the behavior of the model as it deviates away from equilibrium. In much the same way that competitive network growth revolutionized classical network theory, we aim to establish a model which can guide future research into nonequilibrium fluctuation-dissipation by providing a method for interacting with the system in a precise and well-controlled manner as it evolves over time. This model is presented in its present form in Chapter 3. Chapter 2, which covers this work, has been published in Physical Review E as a Rapid Communication [1]. The writing and analysis were performed by me as the primary author. Eric Corwin and Georgios Tsekenis are listed as co-authors for their contribution to the analysis and for advisement on the work. This dissertation includes previously published and unpublished co-authored material.en-USCreative Commons BY-NC-ND 4.0-USNetwork theoryStatistical modelingElectronic Thesis or Dissertation