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

Non-equilibrium umbrella sampling applied to force spectroscopy of soft matter

Physical systems often respond on a timescale which is longer than that of the measurement. This is particularly true in soft matter where direct experimental measurement, for example in force spectroscopy, drives the soft system out of equilibrium and provides a non-equilibrium measure. Here we demonstrate experimentally for the first time that equilibrium physical quantities (such as the mean square displacement) can be obtained from non-equilibrium measurements via umbrella sampling. Our model experimental system is a bead fluctuating in a time-varying optical trap. We also show this for simulated force spectroscopy on a complex soft molecule--a piston-rotaxane

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

Physical activity counseling in overweight and obese primary care patients: Outcomes of the VA-STRIDE randomized controlled trial.

The purpose of this 2-arm randomized clinical trial was to evaluate the effectiveness of a 12-month, expert system-based, print-delivered physical activity intervention in a primary care Veteran population in Pittsburgh, Pennsylvania. Participants were not excluded for many health conditions that typically are exclusionary criteria in physical activity trials. The primary outcome measures were physical activity reported using the Community Healthy Activities Model Program for Seniors (CHAMPS) questionnaire and an accelerometer-based activity assessment at baseline, 6, and 12 months. Of the 232 Veterans enrolled in the study, 208 (89.7%) were retained at the 6-month follow-up and 203 (87.5%) were retained at 12 months. Compared to the attention control, intervention participants had significantly increased odds of meeting the U.S. recommended guideline of ≥ 150 min/week of at least moderate-intensity physical activity at 12 months for the modified CHAMPS (odds ratio [OR] = 2.86; 95% CI: 1.03-7.96; p = 0.04) but not at 6 months (OR = 1.54; 95% CI: 0.56-4.23; p = 0.40). Based on accelerometer data, intervention participants had significantly increased odds of meeting ≥ 150 min/week of moderate-equivalent physical activity at 6 months (OR = 6.26; 95% CI: 1.26-31.22; p = 0.03) and borderline significantly increased odds at 12 months (OR = 4.73; 95% CI: 0.98-22.76; p = 0.053). An expert system physical activity counseling intervention can increase or sustain the proportion of Veterans in primary care meeting current recommendations for moderate-intensity physical activity. Trial Registration Clinical trials.gov identifier: NCT00731094 URL: http://www.clinicaltrials.gov/ct2/show/NCT00731094

Transient State Work Fluctuation Theorem for a Driven Classical System

We derive the nonequilibrium transient state work fluctuation theorem and also the Jarzynski equality for a classical harmonic oscillator linearly coupled to a harmonic heat bath, which is dragged by an external agent. Coupling with the bath makes the dynamics not only dissipative but also non-Markovian in general. Since we do not assume anything about the spectral nature of the harmonic bath the derivation is not only restricted to the Markovian bath rather it is more general, for a non-Markovian bath

Crumpling a Thin Sheet

Crumpled sheets have a surprisingly large resistance to further compression. We have studied the crumpling of thin sheets of Mylar under different loading conditions. When placed under a fixed compressive force, the size of a crumpled material decreases logarithmically in time for periods up to three weeks. We also find hysteretic behavior when measuring the compression as a function of applied force. By using a pre-treating protocol, we control this hysteresis and find reproducible scaling behavior for the size of the crumpled material as a function of the applied force.Comment: revtex 4 pages, 6 eps figures submitted to Phys Rev. let

Dragging a polymer chain into a nanotube and subsequent release

We present a scaling theory and Monte Carlo (MC) simulation results for a flexible polymer chain slowly dragged by one end into a nanotube. We also describe the situation when the completely confined chain is released and gradually leaves the tube. MC simulations were performed for a self-avoiding lattice model with a biased chain growth algorithm, the pruned-enriched Rosenbluth method. The nanotube is a long channel opened at one end and its diameter $D$ is much smaller than the size of the polymer coil in solution. We analyze the following characteristics as functions of the chain end position $x$ inside the tube: the free energy of confinement, the average end-to-end distance, the average number of imprisoned monomers, and the average stretching of the confined part of the chain for various values of $D$ and for the number of monomers in the chain, $N$. We show that when the chain end is dragged by a certain critical distance $x^*$ into the tube, the polymer undergoes a first-order phase transition whereby the remaining free tail is abruptly sucked into the tube. This is accompanied by jumps in the average size, the number of imprisoned segments, and in the average stretching parameter. The critical distance scales as $x^*\sim ND^{1-1/\nu}$. The transition takes place when approximately 3/4 of the chain units are dragged into the tube. The theory presented is based on constructing the Landau free energy as a function of an order parameter that provides a complete description of equilibrium and metastable states. We argue that if the trapped chain is released with all monomers allowed to fluctuate, the reverse process in which the chain leaves the confinement occurs smoothly without any jumps. Finally, we apply the theory to estimate the lifetime of confined DNA in metastable states in nanotubes.Comment: 13pages, 14figure