Statistical physics has been the foundation for much of our understanding about plasma physics. Often, plasma physics phenomena are explained using statistical physics principles and theories. Here, I reverse this paradigm to instead use plasma experiments to test statistical physics principles.
In this thesis, I test statistical physics principles with an experimental dusty plasma, which is a four-component mixture of micron-sized ``dust'' particles, electrons, ions, and neutral gas molecules. When immersed in the plasma, the dust particles acquire large negative charges, since they accumulate more electrons than ions. Due to their large electric charges, the dust particles have interparticle potential energies that greatly exceed their kinetic energies, so that the collection of dust particles is considered to be a strongly coupled plasma. Like other strongly coupled plasma, the collection of dust particles can exhibit solid-like or liquid-like behavior.
A key advantage offered by dusty plasma experiments is the ability to track the motion of individual dust particles. Dust particles are sufficiently large to allow for direct imaging using a video camera, so that time series data can be obtained for particle positions and velocities. These particle-level data provide a richer description of the dynamics and structure than can be obtained for most other strongly coupled plasmas, simple liquids, or solid materials. In particular, the particle-level data of positions and velocities are often required inputs for testing statistical physics theories or principles.
The dusty plasma data I analyze are from the experiment of Haralson~\textit{et al.} [1,2], where dust particles were electrically levitated in a single horizontal layer within a vacuum chamber. The collection of dust particles initially settled into a crystalline lattice with solid-like behavior. To reach a liquid-like state, or to drive a shear flow, dust particles were manipulated using the radiation pressure force of lasers.
In this thesis, I test three different statistical physics principles using an experimental dusty plasma.
First, I test the fluctuation theorem, which was first was presented in 1993 by Evans, Cohen, and Morriss [3]. The fluctuation theorem, which is one of the most important recent developments in statistical physics, quantifies the probability that the entropy production rate will temporarily fluctuate to negative values in ``violations'' of the second law of thermodynamics. The original formulation of the fluctuation theorem described the entropy production due to viscous heating in a shear flow; this version of the fluctuation theorem had never been experimentally demonstrated in a liquid of any kind. In Chapter 2, I provide the first such demonstration by showing that the entropy production rate in a liquid-like dusty plasma shear flow satisfies the fluctuation theorem. This result also serves as the first demonstration that a strongly coupled plasma obeys the fluctuation theorem.
Second, I measure the Einstein frequency $\Omega_E$, which describes the stochastic process of collisions in a strongly coupled plasma, and I compare my measurement to predictions made in the literature that used simulation data. Often, for weakly coupled plasma, a collision frequency is obtained to provide a measure of the strength of particle-particle interactions. However, for strongly coupled plasma (and likewise for liquids and solids), a collision frequency is not well defined since collisions are multibody and occur continuously. Another quantity is needed to describe the strength of particle-particle interactions. I propose that the Einstein frequency $\Omega_E$, a concept more commonly used in solid physics, is better suited for describing particle-particle interactions in a strongly coupled plasma. In Chapter 3, I present and use a new method to obtain the Einstein frequency of a 2D dusty plasma in both a liquid-like state and a crystalline state. My measurement of the Einstein frequency, which serves as a proxy for a collision frequency, is consistent with simulation predictions in the literature.
Third, I present particle-coordination survival functions, which provide a richer description of microscopic dynamics in a liquid than the commonly used relaxation time. Relaxation times have been used, for example the Maxwell relaxation time, to describe the characteristic time scale for the crossover between elastic and viscous behavior in viscoelastic liquids. However, relaxation times are single-value measures that cannot fully describe the complexity of a liquid. In Chapter 4, using a survival function that retains temporal information about the local structural in a liquid, I discover that the microscopic arrangements in a liquid-like 2D dusty plasma have multiple time scales. Unexpectedly, non-defects have two time scales, while defects have one. My survival functions are time-series graphs of the probability that a particle's number of nearest neighbors, i.e., its coordination, remains the same. The two time scales for non-defects are revealed by an elbow in their survival-function curve.
As a spinoff with a considerable amount of importance, I performed the simplest fluctuation theorem experiment to date, using an aerosol. An aerosol is simply a particle that is immersed in air. In Chapter 5, I show that the fluctuation theorem is applicable for an aerosol particle undergoing free-fall in air due to gravity. While the particle typically fell downwards, it is observed to occasionally fall upwards, against the force of gravity. For such upward displacements, the work done on the particle is negative, which is a temporary violation of the second law. I find that the probability of these temporarily violations obeys the work fluctuation theorem. This result also allowed an application: a novel diagnostic method to measure the mass of aerosol particles.