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.

Characterization of Borrelia burgdorferi Gene Product BBD18 for Its Role(s) in Pathogen Biology and Infectivity

bbd18 is a differentially expressed Borrelia burgdorferi gene that is transcribed at almost undetectable levels in spirochetes grown in vitro but dramatically upregulated during tick infection. The gene also displays low yet detectable expression at various times in tissues of murine hosts. As the gene product bears no homology to known proteins, its biological significance remains enigmatic. To understand the gene function, we created isogenic bbd18-deletion mutants as well as genetically-complemented isolates from an infectious wild-type B. burgdorferi strain. Compared to parental isolates, bbd18 mutants - but not complemented spirochetes - displayed slower in vitro growth. The bbd18 mutants also reflect significantly reduced ability to persist or remain undetectable both in immunocompetent and SCID mice, yet were able to survive in ticks. This suggests BBD18 function is essential in mammalian hosts but redundant in the arthropod vector. Notably, although bbd18 expression and in vitro growth defects are restored in the complemented isolates, their phenotype is similar to the mutants - being unable to persist in mice but able to survive in ticks. Despite low expression in cultured wild-type B. burgdorferi, bbd18 deletion downregulated several genes. Interestingly, expression of some, including ospD and bbi39, could be complemented, while that of others could not be restored via bbd18 re-expression. Correspondingly, bbd18 mutants displayed altered production of several proteins, and similar to RNA levels, some were restored in the bbd18 complement and others not. To understand how bbd18 deletion results in apparently permanent and noncomplementable phenotypic defects, we sought to genetically disturb the DNA topology surrounding the bbd18 locus without deleting the gene. Spirochetes with an antibiotic cassette inserted downstream of the gene, between bbd17 and bbd18, were significantly attenuated in mice, while a similar upstream insertion, between bbd18 and bbd19, did not affect infectivity, suggesting that an unidentified cis element downstream of bbd18 may encode a virulence-associated factor critical for infection.