Session H5: Thermodynamics and General Physics

Thermodynamics of a Gravitational Gas with Periodic Boundary Conditions

We study the thermodynamic properties of a one-dimensional gas with one-dimensional gravitational interactions. Periodic boundary conditions are implemented as a modification of the potential consisting of a sum over mirror images (Ewald sum), regularized with an exponential cut-off. As a consequence, each particle carries with it its own background density. Using mean field theory, we show that the system has a phase transition at a critical temperature. Above the critical temperature the gas density is uniform, while below the critical point the system becomes inhomogeneous. Precise, event driven, numerical simulations of the model, which include the caloric curve, equation of state, radial distribution function and largest Lyapunov exponent, confirm the existence of the phase transition, and are in good agreement with the theoretical predictions.   

Persistent entropy current? A third-law paradox

We consider persistent currents at finite temperature induced by the Aharonov-Bohm effect in a multiply connected quantum system threaded by a magnetic flux. In general, both the energy current $I_E$ and the particle current $I_N$ are nonzero in the limit $T\rightarrow 0$, while the entropy of the system $S(T)\rightarrow 0$ as $T\rightarrow 0$, consistent with the third law of thermodynamics. The conventional definition of the heat current is $I_Q=I_E-\mu I_N$, with the entropy current defined as $I_S=I_Q/T$. We show that generically the persistent heat current defined in this way is nonzero in the limit $T\rightarrow 0$, leading to the paradoxical result that $I_S \rightarrow \infty$ as $T\rightarrow 0$ despite the fact that $S(T)\rightarrow 0$ and $I_N$ is finite. This suggests that the conventional definition of heat current is problematic for a quantum system in thermal equilibrium. A curl-free formula for the entropy current is proposed as a possible way out of this paradox.   

The Kelvin Poincare Counterexample to the Equipartition Theorem

The statistical interpretation of the second law of thermodynamics was first introduced independently by Maxwell and Boltzmann. One of the results that follows from their probabilistic approach is the equipartition theorem which was stated by Maxwell in 1878 in the following words: ``In the ultimate state of the system, the average kinetic energy of the two given portions of the system must be in the ratio of the number of degrees of freedom of those portions''.$^{\mathrm{1}}$ Lord Kelvin never accepted this statistical basis for thermodynamics and published a short note describing a simple mechanical system that violated this theorem and therefore cast doubt on the use of probability to derive thermodynamics. Poincare proved that Kelvin's system did in fact obey the equipartition law but gave a simple modification to make the test case a perfect counterexample, which indicates that physicists loyal to Newtonian mechanics already knew that the equipartition theorem was doomed before its comparison with experiment. We will discuss the simple mechanical model and present Poincare's analysis of it. $^{\mathrm{1}}$''On the Average Distribution of Energy in a System of Material Points'', \textit{Cambridge Philosophical Society Transactions} (1878).   

Lorentz Invariance of the Casimir Effect

The Casimir Effect---most simply realized as an attractive force between two parallel, neutral, conductive plates---is usually derived from quantized electromagnetic potentials in the Coulomb gauge, which is not Lorentz invariant. We seek a Lorentz-invariant derivation of the Casimir effect, using the Gupta-Bleuler method for quantizing the field and finding equations of motion for the parallel plates. We compare this approach with the motion obtained in the stationary frame.   

Modeling Quantum Energy Teleportation

Quantum teleportation is a well-established procedure that uses the quantum resources~of entanglement and joint measurement to recover information remotely without ever propagating that information through space and time. In contrast, the idea of quantum \textit{energy }teleportation (QET) has been proposed more recently with both similarities and differences in theory and principles from quantum information teleportation (QIT). I review the principles behind QET and connect Masahiro Hotta's simplified model of QET with QIT. Upon confirming theoretically the ability of successful energy~extraction, I analyze Hotta's model further to understand its basic elements and search for alternate~models to maximize the~energy extraction.   

Fringe Visibility and Which-Way Information: Duality Relations

The principle of wave-particle duality states that quantum objects cannot exhibit full wave and particle characteristics simultaneously. In simple cases such as a two-slit experiment or a Mach-Zehnder interferometer, fringe visibility is limited by the amount of which-way information available. For these cases we quantify the connection between fringe visibility and which-way information. We also study to what extent, for arbitrary which-way schemes, the Heisenberg uncertainty relation has been used to derive these relations in the literature.   

Numerical PDE Coupling for Water Vapor Transport in Baled Corn Stover

Drying baled corn stover is of interest to those in biofuels and agriculture research at Idaho National Laboratory. Dried bales are significantly easier to process in ethanol producing plants, easier to transport, and experience less dry matter loss. We investigate water transport inside a corn stover bale using analytic models and a numerical model of coupled PDEs. Heat exchange between water vapor and liquid water in the bale is considered along with effects from cellular respiration: oxygen diffusion and consumption, heat generation, and liquid water production. Boundary conditions and initial conditions are considered for ambient temperature, oxygen concentration, and humidity. COMSOL Multi-physics allows for high levels of complexity in the model, but as complexity increases, convergence to a solution becomes unreasonably long---changing from minutes to weeks.   

Distributional Tests for the Laser Interferometer Gravitational-Wave Observatory Detections

The Laser Interferometer Gravitational-Wave Observatory (LIGO) advanced-generation detectors started operation in September 2015, heralding the extraordinary discovery of gravitational waves from merging black holes. This detection has opened an era for a new type of astronomy based on hearing the universe, and core-collapse supernovae are one of the most interesting sources to examine. Since the expected signal emitted by supernovae is weak, distributional tests are important tools to analyze the data to determine the existence of evidence of a gravitational wave signal by comparing distributions of background noise triggers and foreground event triggers. To do this, we use nonparametric tests that assume no particular shape of the distributions. Such non-parametric tests include the Kolmogorov-Smirnov, Mann-Whitney, chi squared, and asymmetric chi squared.