Volume 7, Issue 3 - Topical Issue: Advances in statistical physics

We study a strictly scale-invariant probabilistic N-body model with symmetric, uniform, identically distributed random variables. Correlations are induced through a transformation of a multivariate Gaussian distribution with covariance matrix decaying out from the unit diagonal, as ρ/r α for r =1, 2, ..., N-1, where r indicates displacement from the diagonal and where 0 ⩽ ρ ⩽ 1 and α ⩾ 0. We show numerically that the sum of the N dependent random variables is well modeled by a compact support q-Gaussian distribution. In the particular case of α = 0 we obtain q = (1-5/3 ρ) / (1- ρ), a result validated analytically in a recent paper by Hilhorst and Schehr. Our present results with these q-Gaussian approximants precisely mimic the behavior expected in the frame of non-extensive statistical mechanics. The fact that the N → ∞ limiting distributions are not exactly, but only approximately, q-Gaussians suggests that the present system is not exactly, but only approximately, q-independent in the sense of the q-generalized central limit theorem of Umarov, Steinberg and Tsallis. Short range interaction (α > 1) and long range interactions (α < 1) are discussed. Fitted parameters are obtained via a Method of Moments approach. Simple mechanisms which lead to the production of q-Gaussians, such as mixing, are discussed.

We present a view of the non-extensive thermodynamics based on general composition rules. A formal logarithm maps these rules to the addition, which can be used to generate stationary distributions by standard techniques. We review the most commonly used rules and as an application we discuss the Tsallis-Pareto distribution of transverse momenta of energetic hadrons, which emerge from relativistic heavy-ion collisions.

A conditional approach is developed for establishing a generalized thermodynamic-like formalism for superstatistical systems. In this framework, the existence of two largely-separated time scales is explicitly taken into account. A generalization of Einstein’s relation for fluctuations is derived based on the restricted conditional maximum-entropy method.

The notion of a generalized exponential family is considered in the restricted context of non-extensive statistical physics. Examples are given of models belonging to this family. In particular, the q-Gaussians are discussed and it is shown that the configurational probability distributions of the micro-canonical ensemble belong to the q-exponential family.

We reformulate the Gauss’ law of error in presence of correlations which are taken into account by means of a deformed product arising in the framework of the Sharma-Taneja-Mittal measure. Having reviewed the main proprieties of the generalized product and its related algebra, we derive, according to the Maximum Likelihood Principle, a family of error distributions with an asymptotic power-law behavior.

An approach to intermittent systems based on renewal processes is reviewed. The Waiting Times (WTs) between events are the main variables of interest in intermittent systems. A crucial role is played by the class of critical events, characterized by Non-Poisson statistics and non-exponential WT distribution. A particular important case is given by WT distributions with power tail. Critical events play a crucial role in the behavior of a property known as Renewal Aging. Focusing on the role of critical events, the relation between superstatistics and non-homogeneous Poisson processes is discussed, and the role of Renewal Aging is illustrated by comparing a Non-Poisson model with a Poisson one, both of them modulated by a periodic forcing. It is shown that the analysis of Renewal Aging is sensitive to the presence of critical events and that this property can be exploited to detect Non-Poisson statistics in a time series. As a consequence, it is claimed that, apart from the characterization of superstatistical features such as the distribution of the intensive parameter or the separation of the time scales, the Renewal Aging property can give some effort to better determine the role of Non-Poisson critical events in intermittent systems.

We demonstrate that nonextensive perfect relativistic hydrodynamics (q-hydrodynamics) can serve as a model of the usual relativistic dissipative hydrodynamics (d-hydrodynamics) therefore facilitating considerably its applications. As an illustration, we show how using q-hydrodynamics one gets the q-dependent expressions for the dissipative entropy current and the corresponding ratios of the bulk and shear viscosities to entropy density, ζ/s and η/srespectively.

On the basis of statistical mechanics of the Q-Ising model, we formulate the Bayesian inference to the problem of inverse halftoning, which is the inverse process of representing gray-scales in images by means of black and white dots. Using Monte Carlo simulations, we investigate statistical properties of the inverse process, especially, we reveal the condition of the Bayes-optimal solution for which the mean-square error takes its minimum. The numerical result is qualitatively confirmed by analysis of the infinite-range model. As demonstrations of our approach, we apply the method to retrieve a grayscale image, such as standard image Lena, from the halftoned version. We find that the Bayes-optimal solution gives a fine restored grayscale image which is very close to the original. In addition, based on statistical mechanics of the Q-Ising model, we are sucessful in constructing a practically useful method of inverse halftoning using the Bethe approximation.

The spatio-temporal dynamics of three interacting species, two preys and one predator, in the presence of two different kinds of noise sources is studied, by using Lotka-Volterra equations. A correlated dichotomous noise acts on the interaction parameter between the two preys, and a multiplicative white noise affects directly the dynamics of the three species. After analyzing the time behaviour of the three species in a single site, we consider a two-dimensional spatial domain, applying a mean field approach and obtaining the time behaviour of the first and second order moments for different multiplicative noise intensities. We find noise-induced oscillations of the three species with an anticorrelated behaviour of the two preys. Finally, we compare our results with those obtained by using a coupled map lattice (CML) model, finding a good qualitative agreement. However, some quantitative discrepancies appear, that can be explained as follows: i) different stationary values occur in the two approaches; ii) in the mean field formalism the interaction between sites is extended to the whole spatial domain, conversely in the CML model the species interaction is restricted to the nearest neighbors; iii) the dynamics of the CML model is faster since an unitary time step is considered.

We discuss the case of a Brownian particle which is harmonically bound and multiplicatively forced-namely bound by V(x,t)=1/2 a(t)x 2 where a(t)is externally controlled-as another instance that provides a generalization of Onsager-Machlup’s theory to non-equilibrium states, thus allowing establishment of several fluctuation theorems. In particular, we outline the derivation of a fluctuation theorem for work, through the calculation of the work probability distribution as a functional integral over stochastic trajectories.

A monatomic simple liquid in two dimensions, where atoms interact isotropically through the Lennard-Jones-Gauss potential [M. Engel, H.-R. Trebin, Phys. Rev. Lett. 98, 225505 (2007)], is vitrified by the use of a rapid cooling technique in a molecular dynamics simulation. Transformation to a crystalline state is investigated at various temperatures and the time-temperature-transformation (TTT) curve is determined. It is found that the transformation time to a crystalline state is the shortest at a temerature 14% below the melting temperature T m and that at temperatures below T v ≡ 0:6T m the transformation time is much longer than the available CPU time. This indicates that a long-lived glassy state is realized for T ≤ T v.

In this paper we present two simple mathematical models to describe human behavior in reaction to deadlines. When a real commitment (e.g. money) is involved, as in the case of a payment deadline, the expected reaction is to postpone it as close as possible to the deadline to minimize the risk of loosing the value. For low risk commitments this tendency is still present but expected to be looser. In order to test these predictions in a quantitative way, we performed data analysis for the total number of registrations and fee payments vs. time for the recent scientific conference “Statphys 23”, comparing it with the data of another conference in order to recover universal features. Two related models respectively for registrations (weak engagement) and fee payment (strong engagement) are then introduced which are able to explain in a simple way both behaviors, and which show an excellent agreement with real data.

In this paper we discuss how partial knowledge of the density of states for a model can be used to give good approximations of the energy distributions in a given temperature range. From these distributions one can then obtain the statistical moments corresponding to e.g. the internal energy and the specific heat. These questions have gained interest apropos of several recent methods for estimating the density of states of spin models. As a worked example we finally apply these methods to the 3-state Potts model for cubic lattices of linear order up to 128. We give estimates of e.g. latent heat and critical temperature, as well as the micro-canonical properties of interest.

The reactive-wetting process, e.g. spreading of a liquid droplet on a reactive substrate is known as a complex, non-linear process with high sensitivity to minor fluctuations. The dynamics and geometry of the interface (triple line) between the materials is supposed to shed light on the main mechanisms of the process. We recently studied a room temperature reactive-wetting system of a small (∼ 150 μm) Hg droplet that spreads on a thin (∼ 4000 Å) Ag substrate. We calculated the kinetic roughening exponents (growth and roughness), as well as the persistence exponent of points on the advancing interface. In this paper we address the question whether there exists a well-defined model to describe the interface dynamics of this system, by performing two sets of numerical simulations. The first one is a simulation of an interface propagating according to the QKPZ equation, and the second one is a landscape of an Ising chain with ferromagnetic interactions in zero temperature. We show that none of these models gives a full description of the dynamics of the experimental reactivewetting system, but each one of them has certain common growth properties with it. We conjecture that this results from a microscopic behavior different from the macroscopic one. The microscopic mechanism, reflected by the persistence exponent, resembles the Ising behavior, while in the macroscopic scale, exemplified by the growth exponent, the dynamics looks more like the QKPZ dynamics.

The mixed spin-1/2 and spin-1 Ising model on the Bethe lattice with both uniaxial as well as biaxial single-ion anisotropy terms is solved exactly by combining star-triangle and triangle-star mapping transformations with exact recursion relations. Magnetic properties (magnetization, phase diagrams, and compensation phenomenon) are investigated in detail. Particular attention is focused on the effect of uniaxial and biaxial single-ion anisotropies that basically influence the magnetic behavior of the spin-1 atoms.

We rediscuss the entropy of a charged dilaton-axion black hole for both the asymptotically flat and non-flat cases by using the thin film brick-wall model. This improved method avoids some drawbacks in the original brick-wall method such as the small mass approximation, neglecting the logarithm term, and taking the term L 3 as the contribution of the vacuum surrounding the black hole. The entropy we obtain turns out to be proportional to the horizon area of the black hole, conforming to the Bekenstein-Hawking area-entropy formula for black holes.

Non-resonant fusion cross-sections significantly higher than corresponding theoretical predictions are observed in low-energy experiments with deuterated matrix target. Models based on thermal effects, electron screening, or quantum-effect dispersion relations have been proposed to explain these anomalous results: none of them appears to satisfactory reproduce the experiments. Velocity distributions are fundamental for the reaction rates and deviations from the Maxwellian limit could play a central role in explaining the enhancement. We examine two effects: an increase of the tail of the target Deuteron momentum distribution due to the Galitskii-Yakimets quantum uncertainty effect, which broadens the energy-momentum relation; and spatial fluctuations of the Debye-Hückel radius leading to an effective increase of electron screening. Either effect leads to larger reaction rates especially large at energies below a few keV, reducing the discrepancy between observations and theoretical expectations.

We study the effects of time delay on the normalized correlation function C(s) and the associated relaxation time T c for a bistable system with correlations between multiplicative and additive white noises under the condition of small time delay. Using the projection operator method, the expressions of T c and C(s) are obtained. Based on numerical computations, it is found that the delay time τ slows down the rate of fluctuation decay of dynamical variable for the presence of positive feedback intensity (∈ > 0), while speeds up the rate of fluctuation decay of dynamical variable for the presence of negative feedback intensity (∈ < 0). The effects of the delay time τ on the T c and C(s) are entirely opposite for ∈ 〉 0 and ∈ < 0.

The evolutionary dynamics of a system of cancerous cells in a model of chronic myeloid leukemia (CML) is investigated by a statistical approach. Cancer progression is explored by applying a Monte Carlo method to simulate the stochastic behavior of cell reproduction and death in a population of blood cells which can experience genetic mutations. In CML front line therapy is represented by the tyrosine kinase inhibitor imatinib which strongly affects the reproduction of leukemic cells only. In this work, we analyze the effects of a targeted therapy on the evolutionary dynamics of normal, first-mutant and cancerous cell populations. Several scenarios of the evolutionary dynamics of imatinib-treated leukemic cells are described as a consequence of the efficacy of the different modelled therapies. We show how the patient response to the therapy changes when a high value of the mutation rate from healthy to cancerous cells is present. Our results are in agreement with clinical observations. Unfortunately, development of resistance to imatinib is observed in a fraction of patients, whose blood cells are characterized by an increasing number of genetic alterations. We find that the occurrence of resistance to the therapy can be related to a progressive increase of deleterious mutations.

An abstract mathematical framework is presented in this paper as a unification of several deformed or generalized algebra proposed recently in the context of generalized statistical theories intended to treat certain complex thermodynamic or statistical systems. It is shown that, from a mathematical point of view, any bijective function can in principle be used to formulate an algebra in which the conventional algebraic rules are generalized.

We use exact recursion relations to study the magnetic properties of the half-integer mixed spin-5/2 and spin-3/2 Blume-Capel Ising ferromagnetic system on the two-fold Cayley tree that consists of two sublattices A and B. Two positive crystal-field interactions Δ1 and Δ2 are considered for the sublattice with spin-5/2 and spin-3/2 respectively. For different coordination numbers q of the Cayley tree sites, the phase diagrams of the model are presented with a special emphasis on the case q = 3, since other values of q reproduce similar results. First, the T = 0 phase diagram is illustrated in the (D A = Δ1/J,D B = Δ2/J) plane of reduced crystal-field interactions. This diagram shows triple points and coexistence lines between thermodynamically stable phases. Secondly, the thermal variation of the magnetization belonging to each sublattice for some coordination numbers q are investigated as well as the Helmoltz free energy of the system. First-order and second-order phase transitions are found. The second-order phase transitions become sharper and sharper when D A or D B increases. The first-order transitions only exist for some appropriate non-zero values of D A and/or D B. The corresponding transition lines never connect to the second-order transition lines. Thus, the non-existence of tricritical points remains one of the key features of the present model. The magnetic exponent β 0 of the model is estimated and found to be ¼ at small values of D A = D B = D and β 0 = ½ at large values of D. At intermediate values of D, there is a crossover region where the magnetic exponent displays interesting behaviours.

Polyethylene Glycol has an irregular current characteristic under constant voltage and slowly varying relative humidity. The current through a thin film of Gamma-isocyanatopropyltriethoxysilane added Polyethylene glycol (PEG-Si), its hydrogenated and hydrophobically modified forms, as a function of increasing relative humidity at equal time steps is analyzed for chaoticity. We suggest that the irregular behavior of current through PEG-Si thin films as a function of increasing relative humidity could best be analyzed for chaoticity using both time series analysis and detrended uctuation analysis; the relative humidity is kept as a slowly varying parameter. The presence of more then one regime is suggested by the calculation of the maximal Lyapunov exponents. Furthermore, the maximal Lyapunov exponent in each of the regimes was positive, thus confirming the presence of low dimensional chaos. DFA also confirms the presence of at least two different regimes, in agreement with the behavior of the maximal Lyapunov exponent in the time series analysis. We also suggest that the irregular behavior of the current through PEG-Si can be reduced by hydrogenating and hydrophobically modifying PEG-Si and the improvement in stability can be confirmed by our study.

We investigate the critical behavior of one-dimensional (1D) stochastic flow with competing nonlocal and local hopping events, in context of the totally asymmetric simple exclusion process (TASEP) with a defect site in a 1D closed chain. The defect site can effectively generate various boundary conditions, controlling the total number of particles in the system. Both open and periodic-like setups exhibit dynamic instability transitions from a populated finite density phase to an empty road (ER) phase as the nonlocal hopping rate increases. In the stationary populated phase, strong clustering promoted by nonlocal skids drives such transitions and determines their scaling properties. By static and dynamic simulations, we locate such transition points, and discuss their nature and scaling properties. In the open TASEP variant, we numerically establish that the instability transition into the ER phase is second order in the regime where the entry point reservoir controls the current, while it is first order in the regime where the bulk controls the current. Since it is well known that such transitions are absent in the periodic TASEP variant, we compare our results in the open setup with those in the periodic-like setup, and discuss the issue of the ensemble equivalence. Finally, the same discussion is extended to the symmetric cases.

The procedure suggested previously for the description of the square-well (SW) fluid within the framework of the mean spherical approximation is applied to calculate the structure factors of pure Na, pure K, and 0.5Na-0.5K alloy in liquid state. It is shown that our variations of the SW depth and SW width enable us to achieve a good agreement between calculated and experimental structure factors. The procedure under consideration gives more accurate results than the random phase approximation for the same values of the SW parameters.

As an important preceding step for the demonstration of an uncharacteristic (q-deformed) statisticalmechanical structure in the dynamics of the Feigenbaum attractor we uncover previously unknown properties of the family of periodic superstable cycles in unimodal maps. Amongst the main novel properties are the following: i) The basins of attraction for the phases of the cycles develop fractal boundaries of increasing complexity as the period-doubling structure advances towards the transition to chaos. ii) The fractal boundaries, formed by the pre-images of the repellor, display hierarchical structures organized according to exponential clusterings that manifest in the dynamics as sensitivity to the final state and transient chaos. iii) There is a functional composition renormalization group (RG) fixed-point map associated with the family of supercycles. iv) This map is given in closed form by the same kind of q-exponential function found for both the pitchfork and tangent bifurcation attractors. v) There is final-stage ultra-fast dynamics towards the attractor, with a sensitivity to initial conditions which decreases as an exponential of an exponential of time. We discuss the relevance of these properties to the comprehension of the discrete scale-invariance features, and to the identification of the statistical-mechanical framework present at the period-doubling transition to chaos. This is the first of three studies (the other two are quoted in the text) which together lead to a definite conclusion about the applicability of q-statistics to the dynamics associated to the Feigenbaum attractor.

The stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a logistic growth model with correlated noises is studied by using the theory of signal-to-noise ratio (SNR) in the adiabatic limit. The expressions of the SNR are obtained. The effects of multiplicative noise intensity α and additive noise intensity D, and correlated intensity λ on the SNR are discussed respectively. It is found that the existence of a maximum in the SNR is the identifying characteristic of the SR phenomena. In comparison with the SR induced by additive periodic signal, some new features are found: (1) When SNR as a function of λ for fixed ratio of α and D, the varying of α can induce a stochastic multi-resonance, and can induce a re-entrant transition of the peaks in SNR vs λ; (2) There exhibits a doubly critical phenomenon for SNR vs D and λ, i.e., the increasing of D (or λ) can induce the critical phenomenon for SNR with respect to λ (or D); (3) The doubly stochastic resonance effect appears when α and D are simultaneously varying in SNR, i.e., the increment of one noise intensity can help the SR on another noise intensity come forth.

In this paper the driven transport of linear polymers through a nanopore is presented. Biopolymer physical behavior in an external electric field is modeled and its motion is simulated using the Langevin impulse integrator method. Within fairly large limits, the polymer translocation time is inversely proportional with the electric field intensity and directly proportional with the polymer chain length.

We investigate Brownian pump transport in the presence of an unbiased external force. The pumping system is embedded in a finite region bounded by two particle reservoirs. In the adiabatic limit, we obtain the analytical expressions of the current and the concentration ratio. We find that Brownian particles can be pumped through an asymmetric potential from a particle reservoir at low concentration to one at the same or higher concentration in the presence of an unbiased external force.

In this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.

Finding signs of the classical-quantum border is a very important task of perennial interest. We show, using semiclassical arguments, that the frontier between the classical and quantum domains can be characterized by recourse to idiosyncratic features of a delimiter parameter associated with the concepts of i) noise) ii) Husimi distribution functions, iii) Wherl’s entropy, and iv) escort distributions.

Using the generalized uncertainty principle, we calculate the entropy of the charged dilaton-axion black hole for both asymptotically flat and non-flat cases by counting degrees of freedom near the horizon. The divergence of density of states and free energy appearing in the thin film brick-wall model is removed without any cutoff. The entropy proportional to the horizon area is derived from the contribution of the vicinity of the horizon.

Hydrodynamic cavitation is analysed by a global thermodynamics principle following an approach based on the maximum irreversible entropy variation that has already given promising results for open systems and has been successfully applied in specific engineering problems. In this paper we present a new phenomenological method to evaluate the conditions inducing cavitation. We think this method could be useful in the design of turbo-machineries and related technologies: it represents both an original physical approach to cavitation and an economical saving in planning because the theoretical analysis could allow engineers to reduce the experimental tests and the costs of the design process.