[en] The notion of entropic forces often stays mysterious to students, especially to ones coming from outside physics. Although thermodynamics works perfectly in all cases when the notion of entropic force is used, no effort is typically made to explain the mechanical nature of the forces. In this paper we discuss the nature of entropic forces as conditional means of constraint forces in systems where interactions are taken into account as mechanical constraints and discuss several examples of such forces. We moreover demonstrate how these forces appear within the standard formalism of statistical thermodynamics and within the mechanical approach based on the Pope-Ching equation, making evident their connection with the equipartition of energy. The paper is aimed at undergraduate and graduate students studying statistical physics and the teachers teaching it.

[en] The Alexander–Orbach (AO) relation d _w = 2d _f/d _s connecting the fractal dimension of a random walk’s (RW) trajectory d _w or the exponent of anomalous diffusion α = 2/d _w on a fractal structure with the fractal and spectral dimension of the structure itself plays a key role in discussion of dynamical properties of complex systems including living cells and single biomolecules. This relation however does not hold universally and breaks down for some structures like diffusion limited aggregates and Eden trees. We show that the alternative to the AO relation is the explicit dependence of the coefficient of the anomalous diffusion on the system’s size, i.e. the absence of its thermodynamical limit. The prerequisite for its breakdown is the dependence of the local structure of possible steps of the RW on the system’s size. The discussion is illustrated by the examples of diffusion on a Koch curve (AO-conform) and on a Cantor dust (violating AO relation). (paper)

[en] Coherent backscattering of light by optically dense atomic ensembles is considered. The spectrum of scattered radiation is studied. The dynamics of the total intensity and enhancement factor is considered in the case of scattering of pulsed radiation. The spectral and temporal characteristics of coherent backscattering are analysed depending on the observation conditions. As an example, calculations are performed for an ensemble of ⁸⁵Rb atoms in a magnetooptical trap. It is shown that analysis of the correlation and dynamic properties of scattered radiation makes it possible to separate contributions from different orders of scattering and thereby to study the process of radiation trapping in dense media in more detail. (fourth seminar to the memory of d.n. klyshko)

[en] We investigate the stochastic dynamics of an active particle moving at a constant speed under the influence of a fluctuating torque. In our model the angular velocity is generated by a constant torque and random fluctuations described as a Lévy-stable noise. Two situations are investigated. First, we study white Lévy noise where the constant speed and the angular noise generate a persistent motion characterized by the persistence time ${\mathrm{\tau <!--\; ??\; -->}}_D$. At this time scale the crossover from ballistic to normal diffusive behavior is observed. The corresponding diffusion coefficient can be obtained analytically for the whole class of symmetric α-stable noises. As typical for models with noise-driven angular dynamics, the diffusion coefficient depends non-monotonously on the angular noise intensity. As second example, we study angular noise as described by an Ornstein–Uhlenbeck process with correlation time ${\mathrm{\tau <!--\; ??\; -->}}_c$ driven by the Cauchy white noise. We discuss the asymptotic diffusive properties of this model and obtain the same analytical expression for the diffusion coefficient as in the first case which is thus independent on ${\mathrm{\tau <!--\; ??\; -->}}_c$. Remarkably, for ${\mathrm{\tau <!--\; ??\; -->}}_c><!--\; >\; -->{\mathrm{\tau <!--\; ??\; -->}}_D$ the crossover from a non-Gaussian to a Gaussian distribution of displacements takes place at a time ${\mathrm{\tau <!--\; ??\; -->}}_G$ which can be considerably larger than the persistence time ${\mathrm{\tau <!--\; ??\; -->}}_D$. (paper)

[en] We obtain the first passage time density for Levy random processes (LRPs) from a subordination scheme, demonstrating that the first passage time density cannot be inferred uniquely from the probability density function P(x, t) governing the random process. This is due to the fact that P(x, t) does not contain all information on the trajectory of the underlying LRP. (letter to the editor)

[en] In this paper we introduce and analyze a model of a random collection of random oscillators. The model has a random number of oscillators, the oscillators have random amplitudes and random frequencies, and the model’s output is the aggregate of its oscillators’ outputs. Also, the model has two time scales: a ‘human’ time scale, over which the spectral density of the model’s output is measured; and a ‘cosmic’ or a ‘geological’ time scale, over which the model’s random parameters slowly evolve. Analyzing the model we establish that, with respect to the evolution of the oscillators’ frequencies: (i) general random-walk dynamics universally yield white noise, i.e. flat spectral densities; (ii) general geometric random-walk dynamics universally yield 1/f noise, i.e. harmonic spectral densities; and (iii) general Gaussian geometric random-walk dynamics universally yield white noise and flicker noise, i.e. inverse power-law spectral densities. (paper)

[en] Medical surveys regarding the number of heterosexual partners per person yield different female and male averages-a result which, from a physical standpoint, is impossible. In this paper we term this puzzle the 'matchmaking paradox', and establish a statistical model explaining it. We consider a bipartite graph with N male and N female nodes (N >> 1), and B bonds connecting them (B >> 1). Each node is associated a random 'attractiveness level', and the bonds connect to the nodes randomly-with probabilities which are proportionate to the nodes' attractiveness levels. The population's average bonds-per-nodes B/N is estimated via a sample average calculated from a survey of size n (n >> 1). A comprehensive statistical analysis of this model is carried out, asserting that (i) the sample average well estimates the population average if and only if the attractiveness levels possess a finite mean; (ii) if the attractiveness levels are governed by a 'fat-tailed' probability law then the sample average displays wild fluctuations and strong skew-thus providing a statistical explanation to the matchmaking paradox.

[en] Random Walk (RW) is a common numerical tool for modeling the Advection–Diffusion equation. In this work, we develop an improved scheme for incorporating a heterogeneous reaction (i.e., a Robin boundary condition) in a discrete-time RW model. In addition, we apply the approach in two test cases. We compare the improved scheme with the classical as well as with analytical and other numerical solution. We show that the new scheme can reduce the computational error significantly, relative to the first order scheme. This reduction comes at no additional computational cost.

[en] We examine the non-ergodic properties of scaled Brownian motion (SBM), a non-stationary stochastic process with a time dependent diffusivity of the form $D(t)\simeq <!--\; ???\; -->t^{\mathrm{\alpha <!--\; ??\; -->}-<!--\; ???\; -->1}$. We compute the ergodicity breaking parameter EB in the entire range of scaling exponents α, both analytically and via extensive computer simulations of the stochastic Langevin equation. We demonstrate that in the limit of long trajectory lengths T and short lag times Δ the EB parameter as function of the scaling exponent α has no divergence at α = 1/2 and present the asymptotes for EB in different limits. We generalize the analytical and simulations results for the time averaged and ergodic properties of SBM in the presence of ageing, that is, when the observation of the system starts only a finite time span after its initiation. The approach developed here for the calculation of the higher time averaged moments of the particle displacement can be applied to derive the ergodic properties of other stochastic processes such as fractional Brownian motion. (paper)

[en] We discuss the existence of stationary states for subharmonic potentials V(x)∝|x|^c, c < 2, under the action of symmetric α-stable noises. We show analytically that the necessary condition for the existence of the steady state is c > 2 − α. Consequently, for harmonic (c = 2) and superharmonic potentials (c > 2) driven by any α-stable noise, steady states always exist. Stationary states are characterized by probability density functions P(x)∝x^-(c+α-1) for |x|→∞ having a lighter tail than the noise distribution for superharmonic potentials (c > 2) and a heavier tail than the noise distribution for subharmonic ones. Monte Carlo simulations confirm the existence of such stationary states and the form of the tails of the corresponding probability densities