In the late 19th and early 20th centuries famous scientists like Boltzmann, Loschmidt, Maxwell and Einstein tried, unsuccessfully, to find the link between the time-reversible equations of motion of individual molecules and irreversible thermodynamics. The solution to this puzzle was found in 1993, and the link is now known as the Fluctuation Theorem (FT). In the decade that followed theory and computer simulation tested the FT and, in 2002, an experiment indirectly demonstrated the FT.¶ This thesis describes original experiments that demonstrate the FT directly using Optical Tweezers. A related expression, known as the Kawasaki Identity, is also experimentally demonstrated. These experimental results provide a rigorous demonstration that irreversible dynamics can be obtained from a system with time-reversible dynamics.

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.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第20546号 / 理博第4304号 / 新制||理||1618(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 早川 尚男, 教授 川上 則雄, 教授 佐々 真一 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DGAM

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

Nonequilibrium work theorems, such as the Jarzynski equality and the Crooks fluctuation theorem, allow one to use nonequilibrium measurements to determine equilibrium free energies. For example, it has been demonstrated that the Crooks fluctuation theorem can be used to determine RNA folding energies. We used single-molecule manipulation with an atomic force microscope to measure the work done on poly(dA) as it was stretched and relaxed. This single-stranded nucleic acid exhibits unique base-stacking transitions in its force-extension curve due to the strong interactions among A bases, as well as multiple pathways. Here we showed that free energy curves can be determined by using the Crooks fluctuation theorem. The nonequilibrium work theorem can be used to determine free energy curves even when there are multiple pathways.

京都大学 / 0048 / 新制・課程博士 / 博士(理学) / 甲第19472号 / 理博第4132号 / 新制||理||1594(附属図書館) / 32508 / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)教授 佐々 真一, 准教授 藤 定義, 准教授 武末 真二 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

Statistical physics in soft matter systems, physical properties of bio-inspired systems and the mechanical manipulations of nano-systems have been studied using optical tweezers to form the basis of this doctoral Thesis. The first two chapters are on a general introduction about optical tweezers and detailed description of the setup used along with its calibrations. The next three chapters describe studies of statistical properties in soft matter systems, namely, out-of-equilibrium microrheology in a worm-like micellar system, irreversibility to reversibility crossover in the non-equilibrium trajectories of an optically trapped particle with the verification of fluctuation theorems even for non-ergodic descriptions of the system and high velocity Brownian vortexes at the liquid-air interface. The mechanical manipulation of the nano-systems, i.e. optically driven nano-rotors and the trapping, as well as transportation of palladium decorated single wall carbon nanotubes using optical tweezers have been discussed in the next two chapters. In the next chapter, the study of physical property of a bio-inspired system -the cell membrane deformability of human erythrocytes with increasing calcium ion concentration has been described. This Thesis is an endeavor to understand different mesoscopic systems using optical trapping and manipulation. Chapter 1 gives an introduction on optical tweezers. The working principle of optical trapping and manipulation are discussed along with their applicability in different fields of physics. Chapter 2 discusses the experimental setup in detail. The setup used for the experiments is a dual optical trap around an inverted microscope. The formation of the traps, the technique to steer the trapping beams and to place the traps at the desired positions in 3D without affecting the symmetry or stiffness are described. Instantaneous position tracking of the trapped particle is a very crucial part of optical trapping experiments. A tracking beam is used for this purpose and the trapped bead is imaged on a quadrant photo diode which provides the current signals that corresponds to the particle’s position in the focal plane. Then the calibration of the setup using various calibration methods are explained. Calibration of the setup includes the calibration of the position sensing devices, e.g. the quadrant photo diode and the CCD camera attached to the microscope, calibration of the electronic devices, e.g. the stage nano-positioner, nano-tilt mirror mount etc., and finally calibration of the trap stiffnesses (in both X and Y ) at varying laser powers. Precautions taken during the experiments to minimize the artifacts are also mentioned. In Chapter 3, a nonlinear microrheology experiment to probe directional viscoelasticity of a sheared worm-like micellar system has been described. Many wormlike micellar systems exhibit appreciable shear thinning due to shear induced alignment. As the micelles get aligned, introducing directionality in the system, the viscoelastic properties no longer remain isotropic. An optical tweezers based technique enables us to probe the out-of-equilibrium rheological properties of CTAT (cetyltrimethylammonium tosylate, cationic surfactant) system simultaneously along two orthogonal directions -parallel to the applied shear, as well as perpendicular to it. A trapped bead is dragged through the medium (1 wt% CTAT) and the position fluctuations of the bead, along the direction of motion (X) and perpendicular to it (Y ), are recorded in both ‘drive on’ and ‘drive off’ states. While the displacement of the bead along X -in response to the active drag force -carry signature of conventional shear thinning, its spontaneous position fluctuations along Y , following the fluctuation dissipation theorem, provide the loss modulus (G∗∗ along Y ) which manifests a dramatic orthogonal shear thickening, an effect hitherto unobserved. Chapter 4 describes an irreversibility to reversibility crossover in the transient response of a particle in optical trap; and the verification of the fluctuation theorem for a non-ergodic description of this system. The transient position fluctuations of a colloidal bead is studied as it approaches equilibrium after being released from varying heights (by using an additional very strong optical trap) in the potential energy landscape created by a weak optical trap. The time evolution of the system shows dramatic changes as the release point energy is decreased. Starting from a small-time-reversible to long-time-irreversible transition for a higher energy release, a time independent completely reversible state could be reached just by lowering the initial potential energy a bit. For an even lower energy release, the system shows an anomalous irreversibility. In this state, it progressively extracts useful work from the thermal fluctuations and surprisingly goes to a higher energy phase point. Highlighting the competition between the micro-reversibility and the irreversible dissipative loss in determining the long-time system behavior, this study exhibits the prominent emergence of a completely reversible state even at long time, in between the two irreversible states of opposite kind. The Transient Fluctuation Theorem (TFT) and the Integrated Transient Fluctuation Theorem (ITFT) which are defined to be valid only for ergodic systems, have been verified even for non-ergodic descriptions (separately for different release points) of this system. Chapter 5 illustrates the study of high velocity Brownian vortex at the liquid-air interface. A general kind of Brownian vortexes are constituted by applying an external non-conservative force field to a colloidal particle bound by a conservative optical trapping force at a liquid-air interface. As the liquid medium is translated at a constant velocity with the bead trapped at the interface, the drag force near the surface provide enough rotational component to bias the particle’s thermal fluctuations in a circulatory motion. The frequency of that circular motion increases linearly with the stage velocity, while an increment in the trapping laser power shows the opposite effect. The properties of these Brownian vortexes have been studied extensively to demonstrate how the thermal fluctuations and the advection of the bead play their role in the vortex motions, with an inference that the angular velocity of the circulatory motions offer a comparative measure of the interface fluctuations. In Chapter 6 the optical manipulation of asymmetric nanorods that constitutes optically driven nanorotors are described. The light force, irrespective of its polarization, is used to run a simple nanorotor. While the gradient force of a single beam optical trap holds an asymmetric nanorod, the scattering force is utilized to generate a non-zero torque on the nanorod making it rotate about the optic axis. The inherent textural irregularities or morphological asymmetries of the nanorods give birth to chirality which is responsible for generation of the torque under the radiation pressure. A farther study on nanorotors that are more transparent to infra-red (trapping beam) confirms that the scattering force is indeed the origin of the torque. A model is proposed to explain the rotational motion of the nanorods and estimate the speed of rotation. If the nanorods are not fairly transparent to the laser beam, even a small surface irregularity with non-zero chirality is sufficient to produce enough torque for moderate rotational speed. Different sized rotors can be used to set the speed of rotation over a wide range, with fine tuning possible through the variation of the laser power. Chapter 7 discuses optical trapping and transportation of palladium decorated single wall carbon nanotubes (Pd-SWNT). Individual carbon nanotubes being substantially smaller than the wavelength of light are not much responsive to optical manipulation. Decorating those single-walled carbon nanotubes with palladium particles changes that scenario dramatically, making the optical trapping and manipulation much easier. Palladium decorated nanotubes (Pd/SWNTs) have higher effective dielectric constant and are trapped at much lower laser power level with greater ease. In addition to that, an asymmetric line trap makes it possible to transport the Pd decorated SWNTs to a desired distant location in the sample cell. In the asymmetric line trap the Pd/SWNTs are first get attracted by the gradient force and then the scattering force push them away towards the other end of the line trap. In Chapter 8, how the rotational motion of crenated erythrocytes in an optical trap can be used to probe their membrane deformability is explained. When placed in a hypertonic buffer medium, discocytic human erythrocytes are subjected to crenation and take deformed shapes. The deformation of the cells brings in chirality and asymmetries in shape that make them rotate under the scattering force of a linearly polarized optical trap. A change in the deformability of the erythrocytes, due to any internal or environmental factor, is reflected in the rotational speed of the trapped crenated cells. Therefore the average rotational speed and the probability of rotation of the crenated erythrocytes in an optical trap can be considered as a direct signature of their membrane deformability. As an example, the relative increment in erythrocyte membrane rigidity with adsorption of Ca++ ions is examined quantitatively through this approach. The Thesis concludes with a summary of the main results and a brief discussion of the scope of future work in Chapter 9.

The weather dynamics are significantly determined by the motion of the atmosphere and the ocean. This motion is often turbulent, characterized by fluctuations of the flow velocity over wide spatial and temporal scales. This fact, besides limited observability and inaccurate models, impedes the predictability of quantities such as the velocity of winds, which are relevant for the everyday life. One is always interested in improving such predictions - by employing better models or obtaining more information about the system. The Crooks fluctuation theorem is a relation from nonequilibrium thermodynamics, which has its typical applications in nanoscale systems. It quantifies the distribution of imposed work in a process, where the system is pushed out of thermal equilibrium. This distribution is broadened due to the fluctuations of the microscopic degrees of freedom in the system. The fluctuations of the velocity field in turbulent flow suggest the derivation of an analogy of Crooks' theorem for this macroscopic system. The knowledge about the validity of such a relation is additional information, which one in reverse could use to improve predictions about the system. In this thesis both issues are addressed: the derivation of the theorem, and the improvement of predictions. We illustrate the application of Crooks' theorem to hydrodynamic flow within a model of a two-dimensional inviscid and incompressible fluid field, when pushed out of dynamical equilibrium. The flow on a rectangular domain is approximated by the two-dimensional vorticity equation with spectral truncation. In this setting, the equilibrium statistics of the flow can be described through a canonical ensemble with two conserved quantities, kinetic energy and enstrophy. To perturb the system out of equilibrium, we change the shape of the domain according to a protocol, which changes the kinetic energy but leaves the enstrophy constant. This is interpreted as doing work to the system. Evolving along a forward and its corresponding backward process, we find that the distributions of the work performed in these processes satisfy the Crooks relation with parameters derived from the canonical ensembles. We address the issue of prediction in this thesis in a concrete setting: There are examples where the distributions of a variable in the forward and the backward process collapse into one, hence Crooks' theorem relates the distribution of one variable with itself. For a finite data set drawn from such a distribution, we are interested in an estimate of this variable to exceed a certain threshold. We demonstrate that, using the knowledge about Crooks' relation, forecast schemes can be proposed which improve compared to a pure frequency estimate on the data set. The findings are illustrated in three examples, studies of parameters such as exceedance threshold and data set size are presented.