We experimentally demonstrate the fluctuation theorem, which predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales, by following the trajectory of a colloidal particle captured in an optical trap that is translated relative to surrounding water molecules. From each particle trajectory, we calculate the entropy production/consumption over the duration of the trajectory and determine the fraction of second law-defying trajectories. Our results show entropy consumption can occur over colloidal length and time scales.

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.

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.

The statistics of liquid-to-crystal nucleation are studied using an automated lag-time apparatus. A single 500 μL sample of distilled water is repeatedly supercooled to a fixed temperature below its equilibrium freezing temperature, held until freezing occurred, and then thawed. Our raw data is then a set of approximately 300 lag-times for each of three set supercooling temperatures. In each case, a small insoluble AgI crystal was added to ensure heterogeneous nucleation and average nucleation temperatures around ΔT=8 K. The distribution of lag-times is analyzed, and shown to be well approximated by a single exponential decay, with average lag-times in the range of 1000–3000 seconds. This average lag-time decreases markedly at deeper levels of supercooling, and for the present data, this decrease is fit equally well by exponential, power law decay, and classical nucleation functional forms.

International audienceThe 2,7-fluorenyl-bridged Fe(?5-C5Me5)(?2-dppe)[C≡C(2,7-C13H6Bu2)C≡C]Fe(?5-C5Me5)(?2-dppe) (1a), its extended analogue Fe(?5-C5Me5)(?2-dppe)[C≡C(1,4-C6H4)C≡C(2,7-C13H6Bu2)C≡C(1,4-C6H4)C≡C](?5-C5Me5)(?2-dppe)Fe (1b), and the corresponding mononuclear complexes Fe(?5-C5Me5)(?2-dppe)[C≡C(2-C13H7Bu2)] (2a) and Fe(?5-C5Me5)(?2-dppe)[C≡C(1,4-C6H4)C≡C(2-C13H7Bu2)] (2b), which model half of these molecules, have been synthesized and characterized in their various redox states. The molecular wire characteristics of the dinuclear complexes were examined in their mixed-valent states, with progression from 1a[PF6] to 1b[PF6] resulting in a sharp decrease in electronic coupling. The cubic nonlinear optical properties of these species were investigated over the visible and near-IR range, a particular emphasis being placed on their multiphoton absorption properties; the complexes are shown to function as redox-switchable nonlinear chromophores at selected wavelengths, and the more extended derivatives are shown to exhibit the more promising NLO performanc