Comment on "On the Crooks fluctuation theorem and the Jarzynski equality" [J. Chem. Phys. 129, 091101 (2008)]

It has recently been argued that a self-consistency condition involving the Jarzynski equality (JE) and the Crooks fluctuation theorem (CFT) is violated for a simple Brownian process [L. Y. Chen, J. Chem. Phys. 129, 091101 (2008)]. This note adopts the definitions in the original formulation of the JE and CFT and demonstrates the contrary.Comment: 2 page

Unbiased estimators for spatial distribution functions of classical fluids

We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density rho(r) in the vicinity of a fixed solute, and for the pair correlation g(r) of a homogeneous classical fluid. We illustrate the utility of our estimators with numerical examples, which reveal advantages over traditional histogram-based methods of computing such distributions.Comment: 15 pages, includes 3 color figure

Stochastic actions for diffusive dynamics: Reweighting, sampling, and minimization

In numerical studies of diffusive dynamics, two different action functionals are often used to specify the probability distribution of trajectories, one of which requiring the evaluation of the second derivative of the potential in addition to the force. Here it is argued that both actions are equivalent prescriptions for the purposes of reweighting and sampling trajectories, whereas the most probable path is more generally given by the global minimum of the action involving the second derivative term. The answer to this apparent paradox lies in the non-differentiable character of Brownian paths, as well as in the "entropy" associated with a given trajectory.Comment: 9 pages, 6 figures; in press (J. Phys. Chem. B

Free energy surfaces from nonequilibrium processes without work measurement

Recent developments in statistical mechanics have allowed the estimation of equilibrium free energies from the statistics of work measurements during processes that drive the system out of equilibrium. Here a different class of processes is considered, wherein the system is prepared and released from a nonequilibrium state, and no external work is involved during its observation. For such ``clamp-and-release'' processes, a simple strategy for the estimation of equilibrium free energies is offered. The method is illustrated with numerical simulations, and analyzed in the context of tethered single-molecule experiments.Comment: 15 pages, 3 figures (1 color); accepted to J. Chem. Phy

Long-Lived Oscillons from Asymmetric Bubbles: Existence and Stability

The possibility that extremely long-lived, time-dependent, and localized field configurations (“oscillons”) arise during the collapse of asymmetrical bubbles in (2+1)-dimensional φ4 models is investigated. It is found that oscillons can develop from a large spectrum of elliptically deformed bubbles. Moreover, we provide numerical evidence that such oscillons are (a) circularly symmetric and (b) linearly stable against small arbitrary radial and angular perturbations. The latter is based on a dynamical approach designed to investigate the stability of nonintegrable time-dependent configurations that is capable of probing slowly growing instabilities not seen through the usual “spectral” method

Optimized free energies from bidirectional single-molecule force spectroscopy

An optimized method for estimating path-ensemble averages using data from processes driven in opposite directions is presented. Based on this estimator, bidirectional expressions for reconstructing free energies and potentials of mean force from single-molecule force spectroscopy - valid for biasing potentials of arbitrary stiffness - are developed. Numerical simulations on a model potential indicate that these methods perform better than unidirectional strategies.Comment: 4 pages, 2 figure