Onsager-Machlup theory and work fluctuation theorem for a harmonically driven Brownian particle

We extend Tooru-Cohen analysis for nonequilirium steady state(NSS) of a Brownian particle to nonequilibrium oscillatory state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian particle in the presence of an oscillating electric field and prove work fluctuation theorem, which is valid for any initial distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen, work fluctuation theorem is valid for any initial condition(also NSS), but only in large time limit. We use Onsager-Machlup Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate and properties of dissipation functions for the present system using Onsager-Machlup functional.Comment: 6 pages, 1 figur

Effective pair potentials for spherical nanoparticles

An effective description for spherical nanoparticles in a fluid of point particles is presented. The points inside the nanoparticles and the point particles are assumed to interact via spherically symmetric additive pair potentials, while the distribution of points inside the nanoparticles is taken to be spherically symmetric and smooth. The resulting effective pair interactions between a nanoparticle and a point particle, as well as between two nanoparticles, are then given by spherically symmetric potentials. If overlap between particles is allowed, the effective potential generally has non-analytic points, but for each effective potential the expressions for different overlapping cases can be written in terms of one analytic auxiliary potential. Effective potentials for hollow nanoparticles (appropriate e.g. for buckyballs) are also considered, and shown to be related to those for solid nanoparticles. Finally, explicit expressions are given for the effective potentials derived from basic pair potentials of power law and exponential form, as well as from the commonly used London-Van der Waals, Morse, Buckingham, and Lennard-Jones potential. The applicability of the latter is demonstrated by comparison with an atomic description of nanoparticles with an internal face centered cubic structure.Comment: 27 pages, 12 figures. Unified description of overlapping and nonoverlapping particles added, as well as a comparison with an idealized atomic descriptio

Crucial role of sidewalls in velocity distributions in quasi-2D granular gases

Our experiments and three-dimensional molecular dynamics simulations of particles confined to a vertical monolayer by closely spaced frictional walls (sidewalls) yield velocity distributions with non-Gaussian tails and a peak near zero velocity. Simulations with frictionless sidewalls are not peaked. Thus interactions between particles and their container are an important determinant of the shape of the distribution and should be considered when evaluating experiments on a tightly constrained monolayer of particles.Comment: 4 pages, 4 figures, Added reference, model explanation charified, other minor change

An Extension of the Fluctuation Theorem

Heat fluctuations are studied in a dissipative system with both mechanical and stochastic components for a simple model: a Brownian particle dragged through water by a moving potential. An extended stationary state fluctuation theorem is derived. For infinite time, this reduces to the conventional fluctuation theorem only for small fluctuations; for large fluctuations, it gives a much larger ratio of the probabilities of the particle to absorb rather than supply heat. This persists for finite times and should be observable in experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and white

Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces

Heat fluctuations over a time \tau in a non-equilibrium stationary state and in a transient state are studied for a simple system with deterministic and stochastic components: a Brownian particle dragged through a fluid by a harmonic potential which is moved with constant velocity. Using a Langevin equation, we find the exact Fourier transform of the distribution of these fluctuations for all \tau. By a saddle-point method we obtain analytical results for the inverse Fourier transform, which, for not too small \tau, agree very well with numerical results from a sampling method as well as from the fast Fourier transform algorithm. Due to the interaction of the deterministic part of the motion of the particle in the mechanical potential with the stochastic part of the motion caused by the fluid, the conventional heat fluctuation theorem is, for infinite and for finite \tau, replaced by an extended fluctuation theorem that differs noticeably and measurably from it. In particular, for large fluctuations, the ratio of the probability for absorption of heat (by the particle from the fluid) to the probability to supply heat (by the particle to the fluid) is much larger here than in the conventional fluctuation theorem.Comment: 23 pages, 6 figures. Figures are now in color, Eq. (67) was corrected and a footnote was added on the d-dimensional cas

Fronts with a Growth Cutoff but Speed Higher than v∗v^*

Fronts, propagating into an unstable state $\phi=0$, whose asymptotic speed $v_{\text{as}}$ is equal to the linear spreading speed $v^*$ of infinitesimal perturbations about that state (so-called pulled fronts) are very sensitive to changes in the growth rate $f(\phi)$ for $\phi \ll 1$. It was recently found that with a small cutoff, $f(\phi)=0$ for $\phi < \epsilon$, $v_{\text{as}}$ converges to $v^*$ very slowly from below, as $\ln^{-2} \epsilon$. Here we show that with such a cutoff {\em and} a small enhancement of the growth rate for small $\phi$ behind it, one can have $v_{\text{as}} > v^*$, {\em even} in the limit $\epsilon \to 0$. The effect is confirmed in a stochastic lattice model simulation where the growth rules for a few particles per site are accordingly modified.Comment: 4 pages, 4 figures, to appear in Rapid Comm., Phys. Rev.

The association between fast-food outlet proximity and density and Body Mass Index:Findings from 147,027 Lifelines cohort study participants

Unhealthy food environments may contribute to an elevated Body Mass Index (BMI), which is a chronic disease risk factor. We examined the association between residential fast-food outlet exposure, in terms of proximity and density, and BMI in the Dutch adult general population. Additionally, we investigated to what extent this association was modified by urbanisation level. In this cross-sectional study, we linked residential addresses of baseline adult Lifelines cohort participants (N = 147,027) to fast-food outlet locations using geo-coding. We computed residential fast-food outlet proximity, and density within 500 m(m), 1, 3, and 5 km(km). We used stratified (urban versus rural areas) multilevel linear regression models, adjusting for age, sex, partner status, education, employment, neighbourhood deprivation, and address density. The mean BMI of participants was 26.1 (SD 4.3) kg/m2. Participants had a mean (SD) age of 44.9 (13.0), 57.3% was female, and 67.0% lived in a rural area. Having two or more (urban areas) or five or more (rural areas) fast-food outlets within 1 km was associated with a higher BMI (B = 0.32, 95% confidence interval (CI):0.03,0.62; B = 0.23, 95% CI:0.10,0.36, respectively). Participants in urban and rural areas with a fast-food outlet within <250 m had a higher BMI (B = 0.30, 95% CI:0.03,0.57; B = 0.20, 95% CI:0.09,0.31, respectively). In rural areas, participants also had a higher BMI when having at least one fast-food outlet within 500 m (B = 0.10, 95% CI:0.02,0.18). In conclusion, fast-food outlet exposure within 1 km from the residential address was associated with BMI in urban and rural areas. Also, fast-food outlet exposure within 500 m was associated with BMI in rural areas, but not in urban areas. In the future, natural experiments should investigate changes in the fast-food environment over time

The association between the presence of fast-food outlets and BMI:the role of neighbourhood socio-economic status, healthy food outlets, and dietary factors

BACKGROUND: Evidence on the association between the presence of fast-food outlets and Body Mass Index (BMI) is inconsistent. Furthermore, mechanisms underlying the fast-food outlet presence-BMI association are understudied. We investigated the association between the number of fast-food outlets being present and objectively measured BMI. Moreover, we investigated to what extent this association was moderated by neighbourhood socio-economic status (NSES) and healthy food outlets. Additionally, we investigated mediation by frequency of fast-food consumption and amount of fat intake. METHODS: In this cross-sectional study, we used baseline data of adults in Lifelines (N = 149,617). Geo-coded residential addresses were linked to fast-food and healthy food outlet locations. We computed the number of fast-food and healthy food outlets within 1 kilometre (km) of participants' residential addresses (each categorised into null, one, or at least two). Participants underwent objective BMI measurements. We linked data to Statistics Netherlands to compute NSES. Frequency of fast-food consumption and amount of fat intake were measured through questionnaires in Lifelines. Multivariable multilevel linear regression analyses were performed to investigate associations between fast-food outlet presence and BMI, adjusting for individual and environmental potential confounders. When exposure-moderator interactions had p-value < 0.10 or improved model fit (∆AIC ≥ 2), we conducted stratified analyses. We used causal mediation methods to assess mediation. RESULTS: Participants with one fast-food outlet within 1 km had a higher BMI than participants with no fast-food outlet within 1 km (B = 0.11, 95% CI: 0.01, 0.21). Effect sizes for at least two fast-food outlets were larger in low NSES areas (B = 0.29, 95% CI: 0.01, 0.57), and especially in low NSES areas where at least two healthy food outlets within 1 km were available (B = 0.75, 95% CI: 0.19, 1.31). Amount of fat intake, but not frequency of fast-food consumption, explained this association for 3.1%. CONCLUSIONS: Participants living in low SES neighbourhoods with at least two fast-food outlets within 1 km of their residential address had a higher BMI than their peers with no fast-food outlets within 1 km. Among these participants, healthy food outlets did not buffer the potentially unhealthy impact of fast-food outlets. Amount of fat intake partly explained this association. This study highlights neighbourhood socio-economic inequalities regarding fast-food outlets and BMI

Onsager-Machlup theory for nonequilibrium steady states and fluctuation theorems

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integrals for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit.Comment: 20 pages, 2 figure

The Weakly Pushed Nature of "Pulled" Fronts with a Cutoff

The concept of pulled fronts with a cutoff $\epsilon$ has been introduced to model the effects of discrete nature of the constituent particles on the asymptotic front speed in models with continuum variables (Pulled fronts are the fronts which propagate into an unstable state, and have an asymptotic front speed equal to the linear spreading speed $v^*$ of small linear perturbations around the unstable state). In this paper, we demonstrate that the introduction of a cutoff actually makes such pulled fronts weakly pushed. For the nonlinear diffusion equation with a cutoff, we show that the longest relaxation times $\tau_m$ that govern the convergence to the asymptotic front speed and profile, are given by $\tau_m^{-1} \simeq [(m+1)^2-1] \pi^2 / \ln^2 \epsilon$, for $m=1,2,...$.Comment: 4 pages, 2 figures, submitted to Brief Reports, Phys. Rev.