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.

THE TERMINATION PHASE: THERAPISTS’ PERSPECTIVE ON THE THERAPEUTIC RELATIONSHIP AND OUTCOME

The termination phase of treatment is recognized as a significant aspect of the therapy process and yet remains vastly understudied in psychotherapy literature. In the present study, therapists’ perspectives were used to examine how three elements of the therapy relationship (working alliance, real relationship and transference) during the termination phase relate to perceived client sensitivity to loss, termination phase evaluation and overall treatment outcome. Self-report data was gathered from 233 therapists, recruited from two Divisions of the American Psychological Association. Therapists completed measures for their work with a client with whom they could identify a termination phase of treatment. Results revealed that the working alliance and real relationship during the termination phase related positively to termination phase evaluation and overall treatment outcome, whereas negative transference during the termination phase related negatively to overall treatment outcome. Therapists’ perceptions of client sensitivity to loss related positively to both negative and positive transference during the termination phase. Post-hoc analyses revealed only the working alliance during the termination phase uniquely predicted overall treatment outcome in a model with the three therapy relationship elements examined together. On the other hand, all three therapy relationship variables during the termination phase uniquely predicted termination phase evaluation, when examined together. Limitations and implications of these findings are discussed, and recommendations for future study are suggested.