In this dissertation I discuss quantum thermodynamics, networks, and entropy . Aspects of each of these can be found in my three included projects. The first is about restricted qubit networks and how open subsystems can resist thermalization. For this project I constructed a simulation framework that allows networks of up to 16 qubits to be simulated using a density matrix framework. This code was used to understand and quantify the effects of different network topology and evolution rules to understand what types of conditions lead to stable structure formation. The second is about a novel representation of Causal Dynamical Triangulations (CDTs) in two dimensions. With this representation an important property of existing Monte Carlo simulations, ergodicity, can be validated. I also used this representation to create a unique code for studying ensembles of CDTs in 2D. With this code I can investigate the effects of a dillaton field in this framework. My final project is about the effect of network topology on strategy evolution of game theory agents on a network. Expanding on existing work I find that higher dimensional networks can support community formation with a zero sum payout matrix.