Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non--equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.Comment: 21 pages, 11 figures, To appear in Soft Matte

Fluctuation Theorems

Fluctuation theorems, which have been developed over the past 15 years, have resulted in fundamental breakthroughs in our understanding of how irreversibility emerges from reversible dynamics, and have provided new statistical mechanical relationships for free energy changes. They describe the statistical fluctuations in time-averaged properties of many-particle systems such as fluids driven to nonequilibrium states, and provide some of the very few analytical expressions that describe nonequilibrium states. Quantitative predictions on fluctuations in small systems that are monitored over short periods can also be made, and therefore the fluctuation theorems allow thermodynamic concepts to be extended to apply to finite systems. For this reason, fluctuation theorems are anticipated to play an important role in the design of nanotechnological devices and in understanding biological processes. These theorems, their physical significance and results for experimental and model systems are discussed.Comment: A review, submitted to Annual Reviews in Physical Chemistry, July 2007 Acknowledgements corrected in revisio

Note on the Kaplan-Yorke dimension and linear transport coefficients

A number of relations between the Kaplan-Yorke dimension, phase space contraction, transport coefficients and the maximal Lyapunov exponents are given for dissipative thermostatted systems, subject to a small external field in a nonequilibrium stationary state. A condition for the extensivity of phase space dimension reduction is given. A new expression for the transport coefficients in terms of the Kaplan-Yorke dimension is derived. Alternatively, the Kaplan-Yorke dimension for a dissipative macroscopic system can be expressed in terms of the transport coefficients of the system. The agreement with computer simulations for an atomic fluid at small shear rates is very good.Comment: 12 pages, 5 figures, submitted to J. Stat. Phy

Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales

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

Comparison of work fluctuation relations

We compare two predictions regarding the microscopic fluctuations of a system that is driven away from equilibrium: one due to Crooks [J. Stat. Phys. 90, 1481 (1998)] which has gained recent attention in the context of nonequilibrium work and fluctuation theorems, and an earlier, analogous result obtained by Bochkov and Kuzovlev [Zh. Eksp. Teor. Fiz. 72(1), 238247 (1977)]. Both results quantify irreversible behavior by comparing probabilities of observing particular microscopic trajectories during thermodynamic processes related by time-reversal, and both are expressed in terms of the work performed when driving the system away from equilibrium. By deriving these two predictions within a single, Hamiltonian framework, we clarify the precise relationship between them, and discuss how the different definitions of work used by the two sets of authors gives rise to different physical interpretations. We then obtain a extended fluctuation relation that contains both the Crooks and the Bochkov-Kuzovlev results as special cases.Comment: 14 pages with 1 figure, accepted for publication in the Journal of Statistical Mechanic

Large Magnetic Susceptibility Anisotropy of Metallic Carbon Nanotubes

Through magnetic linear dichroism spectroscopy, the magnetic susceptibility anisotropy of metallic single-walled carbon nanotubes has been extracted and found to be 2-4 times greater than values for semiconducting single-walled carbon nanotubes. This large anisotropy is consistent with our calculations and can be understood in terms of large orbital paramagnetism of electrons in metallic nanotubes arising from the Aharonov-Bohm-phase-induced gap opening in a parallel field. We also compare our values with previous work for semiconducting nanotubes, which confirm a break from the prediction that the magnetic susceptibility anisotropy increases linearly with the diameter.Comment: 4 pages, 4 figure

Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle

Recently Wang et al. carried out a laboratory experiment, where a Brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center. This experiment confirmed a theoretically predicted work related integrated (I) Transient Fluctuation Theorem (ITFT), which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state. The corresponding integrated stationary state fluctuation theorem (ISSFT) was not observed. Using an overdamped Langevin equation and an arbitrary motion for the center of the harmonic force, all quantities of interest for these theorems and the corresponding non-integrated ones (TFT and SSFT, resp.) are theoretically explicitly obtained in this paper. While the (I)TFT is satisfied for all times, the (I)SSFT only holds asymptotically in time. Suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the ISSFT could be observed, are given. In addition, a non-trivial long-time relation between the ITFT and the ISSFT was discovered, which could be observed experimentally, especially in the case of a resonant circular motion of the center of the harmonic force.Comment: 20 pages, 3 figure

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

Deep-water macroalgae from the Canary Islands: new records and biogeographical relationships

Due to the geographical location and paleobiogeography of the Canary Islands, the seaweed flora contains macroalgae with different distributional patterns. In this contribution, the biogeographical relations of several new records of deep-water macroalgae recently collected around the Canarian archipelago are discussed. These are Bryopsidella neglecta (Berthotd) Rietema,Discosporangium mesarthrocarpum (Meneghini) Hauck, Hincksia onslowensis (Amsler et Kapraun)P.C. Silva, Syringoderma floridana Henry, Peyssonnelia harveyana J. Agardh, Cryptonemia seminervis(C. Agardh) J. Agardh, Botryodadia wynnei Ballantine, Gloiocladia blomquistii (Searles) R. E.Norris, PIahchrysis peltata (W. R. Taylor) P. Huv4 et H. Huv4, Leptofauchea brasiliensis Joly, and Sarcodiotheca divaricata W. R. Taylor. These new records, especially those in the Florideophyceae,support the strong affinity of the Canary Islands seaweed flora with the warm-temperate Mediterranean-Atlantic region. Some species are recorded for the first time from the east coast of the Atlantic Ocean, enhancing the biogeographic relations of the Canarian marine flora with that of the western Atlantic regions