Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Multiple sulfur isotope fractionations in inorganic aqueous systems

New constraints on isotope fractionation factors in inorganic aqueous sulfur systems based on theoretical and experimental techniques relevant to studies of the sulfur cycle in modern environments and the geologic rock record are presented in this dissertation. These include theoretical estimations of equilibrium isotope fractionation factors utilizing quantum mechanical software and a water cluster model approach for aqueous sulfur compounds that span the entire range of oxidation state for sulfur. These theoretical calculations generally reproduce the available experimental determinations from the literature and provide new constraints where no others are available. These theoretical calculations illustrate in detail the relationship between sulfur bonding environment and the mass dependence associated with equilibrium isotope exchange reactions involving all four isotopes of sulfur. I additionally highlight the effect of isomers of protonated compounds (compounds with the same chemical formula but different structure, where protons are bound to either sulfur or oxygen atoms) on isotope partitioning in the sulfite (S4+) and sulfoxylate (S2+) systems, both of which are key intermediates in oxidation-reduction processes in the sulfur cycle. I demonstrate that isomers containing the highest degree of coordination around sulfur (where protonation occurs on the sulfur atom) have a strong influence on isotopic fractionation factors, and argue that isomerization phenomenon should be considered in models of the sulfur cycle. Additionally, experimental results of the reaction rates and isotope fractionations associated with the chemical oxidation of aqueous sulfide are presented. Sulfide oxidation is a major process in the global sulfur cycle due largely to the sulfide-producing activity of anaerobic microorganisms in organic-rich marine sediments. These experiments reveal relationships between isotope fractionations and reaction rate as a function of both temperature and trace metal (ferrous iron) catalysis that I interpret in the context of the complex mechanism of sulfide oxidation. I also demonstrate that sulfide oxidation is a process associated with a mass dependence that can be described as not conforming to the mass dependence typically associated with equilibrium isotope exchange. This observation has implications for the inclusion of oxidative processes in environmental- and global-scale models of the sulfur cycle based on the mass balance of all four isotopes of sulfur. The contents of this dissertation provide key reference information on isotopic fractionation factors in aqueous sulfur systems that will have far-reaching applicability to studies of the sulfur cycle in a wide variety of natural settings.