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.

AN ENTROPIC THEORY OF DAMAGE WITH APPLICATIONS TO CORROSION-FATIGUE STRUCTURAL INTEGRITY ASSESSMENT

This dissertation demonstrates an explanation of damage and reliability of critical components and structures within the second law of thermodynamics. The approach relies on the fundamentals of irreversible thermodynamics, specifically the concept of entropy generation due to materials degradation as an index of damage. All failure mechanisms that cause degradation, damage accumulation and ultimate failure share a common feature, namely energy dissipation. Energy dissipation, as a fundamental measure for irreversibility in a thermodynamic treatment of non-equilibrium processes, leads to and can be expressed in terms of entropy generation. The dissertation proposes a theory of damage by relating entropy generation to energy dissipation via generalized thermodynamic forces and thermodynamic fluxes that formally describes the resulting damage. Following the proposed theory of entropic damage, an approach to reliability and integrity characterization based on thermodynamic entropy is discussed. It is shown that the variability in the amount of the thermodynamic-based damage and uncertainties about the parameters of a distribution model describing the variability, leads to a more consistent and broader definition of the well know time-to-failure distribution in reliability engineering. As such it has been shown that the reliability function can be derived from the thermodynamic laws rather than estimated from the observed failure histories. Furthermore, using the superior advantages of the use of entropy generation and accumulation as a damage index in comparison to common observable markers of damage such as crack size, a method is proposed to explain the prognostics and health management (PHM) in terms of the entropic damage. The proposed entropic-based damage theory to reliability and integrity is then demonstrated through experimental validation. Using this theorem, the corrosion-fatigue entropy generation function is derived, evaluated and employed for structural integrity, reliability assessment and remaining useful life (RUL) prediction of Aluminum 7075-T651 specimens tested.

THE COMPLETE PRELUDES OF ALEXANDER SCRIABIN: THE EVOLUTION OF HIS REVOLUTIONARY COMPOSITIONAL STYLE

During the second half of the nineteenth century, a series of remarkable advances in musical composition emerged in the works of such innovative spirits as Franz Liszt, Hector Berlioz and Richard Wagner. Their pioneering works exerted an extraordinary impact on the music of the subsequent generation of composers--of disparate nationalities-who were active at the dawn of the 20th century: Including most notably Claude-Achille Debussy, Gustav Mahler, Richard Strauss, and Alexander Nikolayevich Scriabin. These important musical figures, each one leaving an indelible and formative imprint on late-nineteenth century Romantic style, together launched the modern era in music. Scriabin stands alone as a transcendental visionary: His music, initiated in the fashion of Chopin and Liszt, wanders through the realms of Debussy and Wagner, and, ultimately abandoning late Romantic tradition, unlocks the heretofore unforeseen power of atonality, bitonality, polyrhythms and key-signature free compositions. Arguably, Scriabin's compositions count among the most innovative, idiosyncratic and bewitching of all time. The development of Scriabin's groundbreaking compositional style is best understood by means of his piano works, which comprise the majority of his oeuvre. Beyond the larger works-his twelve sonatas, a concerto and a fantasy-Scriabin's piano explorations are also represented by miniature gems: The mazurkas, impromptus, waltzes, poems, a polonaise, etudes, nocturnes, morceaux and, in particular, the preludes. Scriabin's 90 preludes for piano, arranged in several opus numbers, richly exemplify the striking evolution of his ingenious music, his idiosyncratic philosophy and his provocative personality.

King of the Renaissance: Art and Politics at the Neapolitan Court of Ferrante I, 1458-1494

In the second half of the fifteenth century, King Ferrante I of Naples (r. 1458-1494) dominated the political and cultural life of the Mediterranean world. His court was home to artists, writers, musicians, and ambassadors from England to Egypt and everywhere in between. Yet, despite its historical importance, Ferrante’s court has been neglected in the scholarship. This dissertation provides a long-overdue analysis of Ferrante’s artistic patronage and attempts to explicate the king’s specific role in the process of art production at the Neapolitan court, as well as the experiences of artists employed therein. By situating Ferrante and the material culture of his court within the broader discourse of Early Modern art history for the first time, my project broadens our understanding of the function of art in Early Modern Europe. I demonstrate that, contrary to traditional assumptions, King Ferrante was a sophisticated patron of the visual arts whose political circumstances and shifting alliances were the most influential factors contributing to his artistic patronage. Unlike his father, Alfonso the Magnanimous, whose court was dominated by artists and courtiers from Spain, France, and elsewhere, Ferrante differentiated himself as a truly Neapolitan king. Yet Ferrante’s court was by no means provincial. His residence, the Castel Nuovo in Naples, became the physical embodiment of his commercial and political network, revealing the accretion of local and foreign visual vocabularies that characterizes Neapolitan visual culture.