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Full-Text Articles in Mathematics
Analyzing The Von Neumann Entropy Of Contact Networks, Thomas J. Brower
Analyzing The Von Neumann Entropy Of Contact Networks, Thomas J. Brower
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
When modeling the spread of disease, ecologists use ecological or contact networks to model how species interact with their environment and one another. The structure of these networks can vary widely depending on the study, where the nodes of a network can be defined as individuals, groups, or locations among other things. With this wide range of definition and with the difficulty of collecting samples, it is difficult to capture every factor of every population. Thus ecologists are limited to creating smaller networks that both fit their budget as well as what is reasonable within the population of interest. With …
Entropy In Quantum Mechanics And Applications To Nonequilibrium Thermodynamics, Paul Bracken
Entropy In Quantum Mechanics And Applications To Nonequilibrium Thermodynamics, Paul Bracken
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Classical formulations of the entropy concept and its interpretation are introduced. This is to motivate the definition of the quantum von Neumann entropy. Some general properties of quantum entropy are developed, such as the quantum entropy which always increases. The current state of the area that includes thermodynamics and quantum mechanics is reviewed. This interaction shall be critical for the development of nonequilibrium thermodynamics. The Jarzynski inequality is developed in two separate but related ways. The nature of irreversibility and its role in physics are considered as well. Finally, a specific quantum spin model is defined and is studied in …