Generalized canonical ensembles and ensemble equivalence

This paper is a companion article to our previous paper (J. Stat. Phys. 119, 1283 (2005), cond-mat/0408681), which introduced a generalized canonical ensemble obtained by multiplying the usual Boltzmann weight factor $e^{-\beta H}$ of the canonical ensemble with an exponential factor involving a continuous function $g$ of the Hamiltonian $H$. We provide here a simplified introduction to our previous work, focusing now on a number of physical rather than mathematical aspects of the generalized canonical ensemble. The main result discussed is that, for suitable choices of $g$, the generalized canonical ensemble reproduces, in the thermodynamic limit, all the microcanonical equilibrium properties of the many-body system represented by $H$ even if this system has a nonconcave microcanonical entropy function. This is something that in general the standard ($g=0$) canonical ensemble cannot achieve. Thus a virtue of the generalized canonical ensemble is that it can be made equivalent to the microcanonical ensemble in cases where the canonical ensemble cannot. The case of quadratic $g$-functions is discussed in detail; it leads to the so-called Gaussian ensemble.Comment: 8 pages, 4 figures (best viewed in ps), revtex4. Changes in v2: Title changed, references updated, new paragraph added, minor differences with published versio

Bulk Elastic Moduli and Solute Potentials in Leaves of Freshwater, Coastal, and Marine Hydrophytes. Are Marine Plants More Rigid?

Bulk modulus of elasticity (ɛ), depicting the flexibility of plant tissues, is recognized as an important component in maintaining internal water balance. Elevated ɛ and comparatively low osmotic potential (Ψπ) may work in concert to effectively maintain vital cellular water content. This concept, termed the ‘cell water conservation hypothesis’, may foster tolerance for lower soil-water potentials in plants while minimizing cell dehydration and shrinkage. Therefore, the accumulation of solutes in marine plants, causing decreases in Ψπ, play an important role in plant–water relations and likely works with higher ɛ to achieve favourable cell volumes. While it is generally held that plants residing in marine systems have higher leaf tissue ɛ, to our knowledge no study has specifically addressed this notion in aquatic and wetland plants residing in marine and freshwater systems. Therefore, we compared ɛ and Ψπ in leaf tissues of 38 freshwater, coastal and marine plant species using data collected in our laboratory, with additional values from the literature. Overall, 8 of the 10 highest ɛ values were observed in marine plants, and 20 of the lowest 25 ɛ values were recorded in freshwater plants. As expected, marine plants often had lower Ψπ, wherein the majority of marine plants were below −1.0 MPa and the majority of freshwater plants were above −1.0 MPa. While there were no differences among habitat type and symplastic water content (θsym), we did observe higher θsym in shrubs when compared with graminoids, and believe that the comparatively low θsym observed in aquatic grasses may be attributed to their tendency to develop aerenchyma that hold apoplastic water. These results, with few exceptions, support the premise that leaf tissues of plants acclimated to marine environments tend to have higher ɛ and lower Ψπ, and agree with the general tenets of the cell water conservation hypothesis

Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic drag force plus a random forcing whose statistics is of the L\'evy type. In the stationary regime, the probability density of the work is found to have ``fat'' power-law tails which assign a relatively high probability to large fluctuations compared with the case where the random forcing is Gaussian. These tails lead to a strong violation of existing fluctuation theorems, as the ratio of the probabilities of positive and negative work fluctuations of equal magnitude behaves in a non-monotonic way. Possible experiments that could probe these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references added; v3: typos corrected, new conclusion, close to published versio

Brownian motion with dry friction: Fokker-Planck approach

We solve a Langevin equation, first studied by de Gennes, in which there is a solid-solid or dry friction force acting on a Brownian particle in addition to the viscous friction usually considered in the study of Brownian motion. We obtain both the time-dependent propagator of this equation and the velocity correlation function by solving the associated time-dependent Fokker-Planck equation. Exact results are found for the case where only dry friction acts on the particle. For the case where both dry and viscous friction forces are present, series representations of the propagator and correlation function are obtained in terms of parabolic cylinder functions. Similar series representations are also obtained for the case where an external constant force is added to the Langevin equation.Comment: 18 pages, 13 figures (in color

Path integral approach to random motion with nonlinear friction

Using a path integral approach, we derive an analytical solution of a nonlinear and singular Langevin equation, which has been introduced previously by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion of a solid object on a vibrating horizontal surface. We show that the optimal (or most probable) paths of this model can be divided into two classes of paths, which correspond physically to a sliding or slip motion, where the object moves with a non-zero velocity over the underlying surface, and a stick-slip motion, where the object is stuck to the surface for a finite time. These two kinds of basic motions underlie the behavior of many more complicated systems with solid/solid friction and appear naturally in de Gennes' model in the path integral framework.Comment: 18 pages, 3 figure

Superstatistics, thermodynamics, and fluctuations

A thermodynamic-like formalism is developed for superstatistical systems based on conditional entropies. This theory takes into account large-scale variations of intensive variables of systems in nonequilibrium stationary states. Ordinary thermodynamics is recovered as a special case of the present theory, and corrections to it can be systematically evaluated. A generalization of Einstein's relation for fluctuations is presented using a maximum entropy condition.Comment: 16 pages, no figures. The title changed, some explanations and references added. Accepted for publication in Phys. Rev.

Stick-slip motion of solids with dry friction subject to random vibrations and an external field

We investigate a model for the dynamics of a solid object, which moves over a randomly vibrating solid surface and is subject to a constant external force. The dry friction between the two solids is modeled phenomenologically as being proportional to the sign of the object's velocity relative to the surface, and therefore shows a discontinuity at zero velocity. Using a path integral approach, we derive analytical expressions for the transition probability of the object's velocity and the stationary distribution of the work done on the object due to the external force. From the latter distribution, we also derive a fluctuation relation for the mechanical work fluctuations, which incorporates the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published version, typos corrected, references adde

Chaotic Observer-based Synchronization Under Information Constraints

Limit possibilities of observer-based synchronization systems under information constraints (limited information capacity of the coupling channel) are evaluated. We give theoretical analysis for multi-dimensional drive-response systems represented in the Lurie form (linear part plus nonlinearity depending only on measurable outputs). It is shown that the upper bound of the limit synchronization error (LSE) is proportional to the upper bound of the transmission error. As a consequence, the upper and lower bounds of LSE are proportional to the maximum rate of the coupling signal and inversely proportional to the information transmission rate (channel capacity). Optimality of the binary coding for coders with one-step memory is established. The results are applied to synchronization of two chaotic Chua systems coupled via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference

Early risk factors of overweight developmental trajectories during middle childhood

Background Research is needed to identify early life risk factors associated with different developmental paths leading to overweight by adolescence. Objectives To model heterogeneity in overweight development during middle childhood and identify factors associated with differing overweight trajectories. Methods Data was drawn from the Quebec Longitudinal Study of Child Development (QLSCD; 1998- 2010). Trained research assistants measured height and weight according to a standardized protocol and conducted yearly home interviews with the child’s caregiver (mother in 98% of cases). Information on several putative early life risk factors for the development of overweight were obtained, including factors related to the child’s perinatal, early behavioral family and social environment. Group-based trajectories of the probability of overweight (6- 12 years) were identified with a semiparametric method (n=1678). Logistic regression analyses were used to identify early risk factors (5 months- 5 years) associated with each trajectory. Results Three trajectories of overweight were identified: “early-onset overweight” (11.0 %), “lateonset overweight” (16.6%) and “never overweight” (72.5%). Multinomial analyses indicated that children in the early and late-onset group, compared to the never overweight group, had 3 common types of risk factors: parental overweight, preschool overweight history, and large size for gestational age. Maternal overprotection (OR= 1.12, CI: 1.01-1.25), short nighttime sleep duration (OR=1.66, CI: 1.07-2.57), and immigrant status (OR=2.01, CI: 1.05-3.84) were factors specific to the early-onset group. Finally, family food insufficiency (OR=1.81, CI: 1.00-3.28) was weakly associated with membership in the late-onset trajectory group. Conclusions The development of overweight in childhood follows two different trajectories, which have common and distinct risk factors that could be the target of early preventive interventions