Work probability distribution and tossing a biased coin

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modelling other physical phenomena where rare events play an important role.Comment: 6 pages, 4 figures

Assembly and force measurement with SPM-like probes in holographic optical tweezers

We report a high fidelity tomographic reconstruction of the quantum state of photon pairs generated by parametric down-conversion with orbital angular momentum (OAM) entanglement. Our tomography method allows us to estimate an upper and lower bound for the entanglement between the down-converted photons. We investigate the two-dimensional state subspace defined by the OAM states ±ℓ and superpositions thereof, with ℓ=1, 2, ..., 30. We find that the reconstructed density matrix, even for OAMs up to around ℓ=20, is close to that of a maximally entangled Bell state with a fidelity in the range between F=0.979 and F=0.814. This demonstrates that, although the single count-rate diminishes with increasing ℓ, entanglement persists in a large dimensional state space

Reversibility in nonequilibrium trajectories of an optically trapped particle

The measure of irreversibility as the dissipation function that serves as the quantitative argument in the fluctuation theorem (FT) was investigated. The FT describes the system's thermodynamic irreversibility developed in time from a completely thermodynamically reversibble system at short times to a thermodynamically irreversible one at infinitely long times. It was observed that the ensemble average of ωt was positive definite irrespective of the system for which it was constructed. It was found that the different expressions for ωt can arise in stochastic and deterministic systems

Non-spherical optically trapped probes: Design, control, and applications

In this proceedings paper we show describe how a microtool can be assembled, and tracked in three dimensions such that its full rotational and translational coordinates, q, are recovered. This allows tracking of the motion of any arbitrary point, d, on the microtool's surface. When the micro-tool is held using multiple optical traps the motion of such a point investigates the inside of an ellipsoidal volume - we term this a 'thermal ellipsoid. We demonstrate how the shape of this thermal ellipsoid may be controlled by varying the relative trapping power of the optical traps, and adjusting the angle at which the micro-tool is held relative to the focal plane. Our experimental results follow the trends derived by Simpson and Hanna

Special Lagrangian cones with higher genus links

For every odd natural number g=2d+1 we prove the existence of a countably infinite family of special Lagrangian cones in C^3 over a closed Riemann surface of genus g, using a geometric PDE gluing method.Comment: 48 page

Employee Stock Ownership and Financial Performance in European Countries: The Moderating Effects of Uncertainty Avoidance and Social Trust

This study investigates how the effect of employee stock ownership on financial performance may hinge on the diverse cultural and societal contexts of European countries. Based on agency and national culture theories, we hypothesize that the positive relationship between employee stock ownership and return on assets (ROA) is stronger in those nations with lower uncertainty avoidance and higher social trust. Using a multisource, time‐lagged, large‐scale dataset of 1,741 firms from 21 countries in Europe, our multilevel, random coefficient modeling analysis found evidence for these hypotheses, suggesting that uncertainty avoidance and social trust serve as important contextual cues in predicting the linkage between employee stock ownership and financial performance. Our supplemental analysis with distinction between the managerial and nonmanagerial employee stock ownership further indicates managerial employee stock ownership has a direct positive effect on ROA. Although nonmanagerial employee stock ownership had a nonsignificant association with ROA, the relationship was positive and significant when uncertainty avoidance was low and social trust was high. This research contributes to the existing literature by illuminating some of the contextual influences altering the effectiveness of employee stock ownership. Our findings also offer practical suggestions for effectively using employee stock ownership

Shape-induced force fields in optical trapping

Advances in optical tweezers, coupled with the proliferation of two-photon polymerization systems, mean that it is now becoming routine to fabricate and trap non-spherical particles. The shaping of both light beams and particles allows fine control over the flow of momentum from the optical to mechanical regimes. However, understanding and predicting the behaviour of such systems is highly complex in comparison with the traditional optically trapped microsphere. In this Article, we present a conceptually new and simple approach based on the nature of the optical force density. We illustrate the method through the design and fabrication of a shaped particle capable of acting as a passive force clamp, and we demonstrate its use as an optically trapped probe for imaging surface topography. Further applications of the design rules highlighted here may lead to new sensors for probing biomolecule mechanics, as well as to the development of optically actuated micromachines

An optically actuated surface scanning probe

We demonstrate the use of an extended, optically trapped probe that is capable of imaging surface topography with nanometre precision, whilst applying ultra-low, femto-Newton sized forces. This degree of precision and sensitivity is acquired through three distinct strategies. First, the probe itself is shaped in such a way as to soften the trap along the sensing axis and stiffen it in transverse directions. Next, these characteristics are enhanced by selectively position clamping independent motions of the probe. Finally, force clamping is used to refine the surface contact response. Detailed analyses are presented for each of these mechanisms. To test our sensor, we scan it laterally over a calibration sample consisting of a series of graduated steps, and demonstrate a height resolution of ∼ 11 nm. Using equipartition theory, we estimate that an average force of only ∼ 140 fN is exerted on the sample during the scan, making this technique ideal for the investigation of delicate biological samples

Insights into the Second Law of Thermodynamics from Anisotropic Gas-Surface Interactions

Thermodynamic implications of anisotropic gas-surface interactions in a closed molecular flow cavity are examined. Anisotropy at the microscopic scale, such as might be caused by reduced-dimensionality surfaces, is shown to lead to reversibility at the macroscopic scale. The possibility of a self-sustaining nonequilibrium stationary state induced by surface anisotropy is demonstrated that simultaneously satisfies flux balance, conservation of momentum, and conservation of energy. Conversely, it is also shown that the second law of thermodynamics prohibits anisotropic gas-surface interactions in "equilibrium", even for reduced dimensionality surfaces. This is particularly startling because reduced dimensionality surfaces are known to exhibit a plethora of anisotropic properties. That gas-surface interactions would be excluded from these anisotropic properties is completely counterintuitive from a causality perspective. These results provide intriguing insights into the second law of thermodynamics and its relation to gas-surface interaction physics.Comment: 28 pages, 11 figure