The puzzle of how time-reversible microscopic equations of mechanics lead to the time-irreversible macroscopic equations of thermodynamics has been a paradox since the days of Boltzmann. Boltzmann simply sidestepped this enigma by stating "as soon as one looks at bodies of such small dimension that they contain only very few molecules, the validity of this theorem [the second law of thermodynamics and its description of irreversibility] must cease." Today we can state that the transient fluctuation theorem (TFT) of Evans and Searles is a generalized, second-law-like theorem that bridges the microscopic and macroscopic domains and links the time-reversible and irreversible descriptions. We apply this theorem to a colloidal particle in an optical trap. For the first time, we demonstrate the TFT in an experiment and show quantitative agreement with Langevin dynamics.

Advances in optical tweezers, coupled with the proliferation of 2-photon polymerisation 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 paper 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; 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 bio-molecule mechanics, as well as to the development of optically actuated micro-machines.It is well known that the high intensity gradients generated in a tightly focused laser beam can be used to trap and manipulate micron-sized particles [1]. An optically trapped sphere is an elegant example of a microscopic harmonic oscillator, capable of measuring fN-scale forces, which has proved invaluable for the study of molecular motors and single biopolymer mechanics [2]. However, there are other desirable features of a force field that can only be introduced by modifying the particle shape or dielectric structure beyond that of a simple homogeneous sphere [3,4]. For example, optical torques can be applied to a particle whose symmetry has been lowered either by shape modification With increasing complexity of shape, the problem of predicting, and optimising, the 2 force profile of the trapped particle becomes ever more challenging. Although specialised software packages are available to compute the optical forces [13], their use is not routine.In this paper, therefore, we address this problem and describe a straightforward method for predicting the optical forces acting on extended dielectric particles of general shape. We support the description with rigorous 3-dimensional T-matrix calculations. To illustrate the approach, we describe the design and fabrication of a passive force clamp based on a tapered cylinder and capable of applying a constant force over displacements of several microns. We demonstrate its use in an optically-controlled scanning probe microscope for ultra-low force imaging. Potential future applications of this device may include the imaging of sensitive biological membranes. Results Background theory

The fluctuation theorem ͑FT͒ quantifies the probability of second law violations in small systems over short time scales. While this theorem has been experimentally demonstrated for systems that are perturbed from an initial equilibrium state, there are a number of studies suggesting that the theorem applies asymptotically in the long time limit to systems in a nonequilibrium steady state. The asymptotic application of the FT to such nonequilibrium steady states has been referred to in the literature as the steady-state fluctuation theorem ͑or SSFT͒. In this paper, we demonstrate experimentally the application of the FT to nonequilibrium steady states, using a colloidal particle localized in a translating optical trap. Furthermore, we show, for this colloidal system, that the FT holds under nonequilibrium steady states for all time, and not just in the long time limit, as in the SSFT.

We present an imaging technique using an optically trapped cigar-shaped probe controlled using holographic optical tweezers. The probe is raster scanned over a surface, allowing an image to be taken in a manner analogous to scanning probe microscopy (SPM), with automatic closed loop feedback control provided by analysis of the probe position recorded using a high speed CMOS camera. The probe is held using two optical traps centred at least 10 µm from the ends, minimizing laser illumination of the tip, so reducing the chance of optical damage to delicate samples. The technique imparts less force on samples than contact SPM techniques, and allows highly curved and strongly scattering samples to be imaged, which present difficulties for imaging using photonic force microscopy. To calibrate our technique, we first image a known sample--the interface between two 8 µm polystyrene beads. We then demonstrate the advantages of this technique by imaging the surface of the soft alga Pseudopediastrum. The scattering force of our laser applied directly onto this sample is enough to remove it from the surface, but we can use our technique to image the algal surface with minimal disruption while it is alive, not adhered and in physiological conditions. The resolution is currently equivalent to confocal microscopy, but as our technique is not diffraction limited, there is scope for significant improvement by reducing the tip diameter and limiting the thermal motion of the probe.