This thesis discusses sphere partition functions and their relations to de Sitter (dS) thermodynamics. Quantum states can be modeled by a particle in a 3D box with side lengths a, b, and c: n. ![]() Assume that gas is confined in a three-dimensional volume. Lets see how you can calculate entropy S using the partition function: S k ln ( Z ) + U T Here U stands for internal energy that can be derived from the. With the vision of narrowing the search of such a model with quantum-corrected macroscopic data, we aim to exactly compute the leading quantum (1-loop) corrections to the Gibbons-Hawking entropy, mathematically defined as the logarithm of the effective field theory path integral expanded around the round sphere saddle, i.e. Translational energy levels are very closely spaced, thus, at normal temperatures, large numbers of them are typically accessible. Understanding the statistical origin of these thermodynamic quantities requires a precise microscopic model for the de Sitter horizon. A semi-classical gravity analysis by Gibbons and Hawking implies that the de Sitter horizon has a temperature and entropy, obeying laws of thermodynamics. Due to the exponential cosmic expansion, a static observer in a de Sitter space is surrounded by a horizon. where Z is the partition function for the N -molecule system. ![]() where E is the system energy and z is the molecular partition function. 2021 Theses Doctoral Sphere partition functions and quantum de Sitter thermodynamicsÄriven by a tiny positive cosmological constant, our observable universe asymptotes into a casual patch in de Sitter space in the distant future. In Chapter 21, our analysis of a system of N distinguishable and non-interacting molecules finds that the system entropy is given by.
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