Many thermodynamic relations involve inequalities, with equality if a process does not involve dissipation. In this article we provide equalities in which the dissipative contribution is shown to involve the relative entropy (also called the Kullback-Leibler divergence). The processes considered are general time evolutions in both classical and quantum mechanics, and the initial state is sometimes thermal, sometimes partially so. As an application, the relative entropy is related to transport coefficients.

We study the distribution of dynamical quantities in various one-dimensional disordered models, the critical behavior of which is described by an infinite randomness fixed point. In the disordered contact process, the survival probability $\mathcal{P}\left(t\right)$ is found to show multiscaling in the critical point, meaning that $\mathcal{P}\left(t\right)=t^{-\delta }$, where the (environment and time-dependent) exponent $\delta$ has a universal limit distribution when $t\to \infty$. The limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi-infinite lattice, where it is found to be exponential, while, in the infinite system, conjectures on its limiting behaviors for small and large $\delta$, which are based on numerical results, are formulated. By the same method, the survival probability in the problem of random walks in random environments is also shown to exhibit multiscaling with an exponential limit distribution. In addition to this, the (imaginary-time) spin-spin autocorrelation function of the random transverse-field Ising chain is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach. Consequently, a relationship between the corresponding limit distributions in the two problems can be established. Finally, the distribution of the spontaneous magnetization in this model is also discussed.

Based on the supposition related to fractal nature of transport processes in ion-conducting materials, an expression for the low-frequency ac conductivity dependence was derived. This expression for the ac conductivity generalizes the power-law dependence and gives a possibility to take into account the influence of the electrode polarization effect. The ac conductivity expression obtained is in excellent agreement with experimental data for a wide frequency range.

The differences in phase behavior of anionic silica nanoparticles (88 Å) in the presence of two globular proteins [cationic lysozyme (molecular weight (MW) 14.7 kD) and anionic bovine serum albumin (BSA) (MW 66.4 kD)] have been studied by small-angle neutron scattering. The measurements were carried out on a fixed concentration (1 wt %) of Ludox silica nanoparticles with varying concentrations of proteins (0–5 wt %) at $p$H = 7. It is found that, despite having different natures (opposite charges), both proteins can render to the same kind of aggregation of silica nanoparticles. However, the concentration regions over which the aggregation is observed are widely different for the two proteins. Lysozyme with very small amounts (e.g., 0.01 wt %) leads to the aggregation of silica nanoparticles. On the other hand, silica nanoparticles coexist with BSA as independent entities at low protein concentrations and turn to aggregates at high protein concentrations (>1 wt %). In the case of lysozyme, the charge neutralization by the protein on the nanoparticles gives rise to the protein-mediated aggregation of the nanoparticles. The nanoparticle aggregates coexist with unaggregated nanoparticles at low protein concentrations, whereas, they coexist with a free protein at higher protein concentrations. For BSA, the nonadsorbing nature of the protein produces the depletion force that causes the aggregation of the nanoparticles at higher protein concentrations. The evolution of the interaction is modeled by the two Yukawa potential, taking account of both attractive and repulsive terms of the interaction in these systems. The nanoparticle aggregation is found to be governed by the short-range attraction for lysozyme and the long-range attraction for BSA. The aggregates are characterized by the diffusion limited aggregate type of mass fractal morphology.

The stability of a thin liquid film of an electrolyte on a solid substrate is investigated. In the framework of the Debye-Hückel approximation, we show that the commonly used approximation of fixed potential at the solid-liquid interface does not lead to predictions of film rupture. To reconcile the model with experimental observations, we consider the constant charge density approximation for the solid substrate and then proceed to systematically investigate the effects of charge regulation based on a linear relationship between charge density and potential. Stability criteria are formulated in terms of charge regulation parameters and electrolyte properties, resulting in different types of stability diagrams. Critical thickness below which the film ruptures is shown to decrease as the charge regulation at the solid-liquid interface becomes stronger.

We have identified a metastable liquid-crystal (LC) structure in the de Vries smectic-$A^{*}$ phase (de Vries Sm-$A^{*}$) formed by silicon-containing molecules under certain boundary conditions. The phase transition with the metastable structure was observed in a LC droplet placed on a planar aligned substrate and LCs confined in the groove of a silicon microchannel. During the rapid cooling step, a batonnet structure was generated as an intermediate and metastable state prior to the transition that yielded the thermodynamically stable toric focal conic domains. This distinctive behavior was characterized using depolarized reflection light microscopy and grazing incidence x-ray diffraction techniques. We concluded that the silicon groups in the molecules that formed the de Vries phase induced the formation of layered clusters called cybotactic structures. This observation is relevant to an exploration of the physical properties of cybotactic de Vries phases and gives a hint as to their optoelectronic applications.

The electric-field-induced phase transition of a chiral liquid crystal containing Br revealed a transition phase between the three-layer periodicity ferrielectric phase and the synclinic ferroelectric phase in the electric field versus temperature phase diagram. Resonant x-ray scattering from the transition phase showed a diffuse streak or spotty weak reflections, which were composed of strong $m$/3-order (where $m$ = 1 and 2) reflections and other weak peaks. The spotty reflections were found to be related to a 12-layer periodicity phase with a weak contribution from the 15-layer periodicity. An x-ray intensity analysis based on the Ising model suggested that the 12-layer periodicity phase was composed of two three-layer ferrielectric blocks and six synclinic layers. This model indicated that, in the transition phase, the three-layer ferrielectric molecular configuration gradually changed to the synclinic configuration. The diffuse streak appearing around $m$/3-order reflections near the field-induced transition from the four-layer periodicity phase to the synclinic ferroelectric phase is also discussed.

We performed measurements of the dielectric constants, splay elastic constant, and rotational viscosity of the nematic phase of mixtures of 4,4${}^{\prime }$-$n$-octyl-cyanobiphenyl (8CB) and biphenyl (BP). In contrast with previous results of DasGupta et al. [Phys. Rev. E 63, 041703 (2001); Phys. Lett. A 288, 323 (2001)], we do not find any anomaly of these constants when the smectic-A phase is approached at all concentrations of BP. These results are compatible with recent calorimetric measurements of Denolf et al. [Phys. Rev. Lett. 97, 107801 (2006); Phys. Rev. E 76, 051702 (2007)] and the absence of a tricritical point in the phase diagram. The origin of the anomalies observed by DasGupta et al. at large concentration of BP is also briefly discussed and a likely explanation in terms of biphenyl evaporation is proposed.

In the presence of adenosine triphosphate, molecular motors generate active force dipoles that drive suspensions of protein filaments far from thermodynamic equilibrium, leading to exotic dynamics and pattern formation. Microscopic modeling can help to quantify the relationship between individual motors plus filaments to organization and dynamics on molecular and supramolecular length scales. Here, we present results of extensive numerical simulations of active gels where the motors and filaments are confined between two infinite parallel plates. Thermal fluctuations and excluded-volume interactions between filaments are included. A systematic variation of rates for motor motion, attachment, and detachment, including a differential detachment rate from filament ends, reveals a range of nonequilibrium behavior. Strong motor binding produces structured filament aggregates that we refer to as asters, bundles, or layers, whose stability depends on motor speed and differential end detachment. The gross features of the dependence of the observed structures on the motor rate and the filament concentration can be captured by a simple one-filament model. Loosely bound aggregates exhibit superdiffusive mass transport, where filament translocation scales with lag time with nonunique exponents that depend on motor kinetics. An empirical data collapse of filament speed as a function of motor speed and end detachment is found, suggesting a dimensional reduction of the relevant parameter space. We conclude by discussing the perspectives of microscopic modeling in the field of active gels.

Frequency modulation is a salient acoustic feature of birdsong. Its control is usually attributed to the activity of syringeal muscles, which affect the tension of the labia responsible for sound production. We use experimental and theoretical tools to test the hypothesis that for birds producing tonal sounds such as domestic canaries (Serinus canaria), frequency modulation is determined by both the syringeal tension and the air sac pressure. For different models, we describe the structure of the isofrequency curves, which are sets of parameters leading to sounds presenting the same fundamental frequencies. We show how their shapes determine the relative roles of syringeal tension and air sac pressure in frequency modulation. Finally, we report experiments that allow us to unveil the features of the isofrequency curves.

How does connectivity impact network dynamics? We address this question by linking network characteristics on two scales. On the global scale, we consider the coherence of overall network dynamics. We show that such global coherence in activity can often be predicted from the local structure of the network. To characterize local network structure, we use “motif cumulants,” a measure of the deviation of pathway counts from those expected in a minimal probabilistic network model. We extend previous results in three ways. First, we give acombinatorial formulation of motif cumulants that relates to the allied concept in probability theory. Second, we show that the link between global network dynamics and local network architecture is strongly affected by heterogeneity in network connectivity. However, we introduce a network-partitioning method that recovers a tight relationship between architecture and dynamics. Third, for a particular set of models, we generalize the underlying theory to treat dynamical coherence at arbitrary orders (i.e., triplet correlations and beyond). We show that at any order, only a highly restricted set of motifs impacts dynamical correlations.

Fragmentation of particle swarms into isolated subgroups occurs when interaction forces are weak or restricted. In the restricted case, the swarm experiences the onset of bottlenecks in the graph of interactions that can lead to the fragmentation of the system into subgroups. This work investigates the characteristics of such bottlenecks when the number of particles in the swarm increases. It is shown that certain characteristics of the bottleneck can be captured by considering only the number of particles in the swarm. Considering the case of a connected communication graph constructed in the hypothesis that each particle is influenced by a fixed number of neighboring particles, a limit case is determined for which a lower limit to the Cheeger constant can be derived analytically without the need for extensive algebraic calculations. Results show that as the number of particles increases, the Cheeger constant decreases. Although ensuring a minimum number of interactions per particle is sufficient, in theory, to ensure cohesion, the swarm may face fragmentation as more particles are added to the swarm.

Following the development of a new class of self-sustained oscillators with a time-varying but stable frequency, the inverse approach to these systems is now formulated. We show how observed data arranged in a single-variable time series can be used to recognize such systems. This approach makes use of time-frequency domain information using the wavelet transform as well as the recently developed method of Bayesian-based inference. In addition, a set of methods, named phase fluctuation analysis, is introduced to detect the defining properties of the new class of systems by directly analyzing the statistics of the observed perturbations.We apply these methods to numerical examples but also elaborate further on the cardiac system.

We study the synchronization and frequency distribution in networks of time-delayed Kuramoto oscillators with identical natural frequency. It is found that a pronounced frequency dispersion occurs in networks with nonidentical degree distributions. The deviation of the average network frequency from its natural frequency, induced by the time delay, is identified as a necessary component for this phenomenon. Altogether this results in states intermediate between perfect synchronization and complete incoherence.

We explore both analytically and numerically an ensemble of coupled phase oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time delay (due to finite signal-propagation speeds) and network plasticity (via dynamic coupling constants) inspired by the Hebbian learning rule in neuroscience. When time delay and learning effects combine, interesting synchronization phenomena are observed. We investigate the formation of spatiotemporal patterns in both one- and two-dimensional oscillator lattices with periodic boundary conditions and comment on the role of dimensionality.

We perform classical three-dimensional Monte Carlo simulations of ultracold neutrons scattering through an absorbing-reflecting mirror system in the Earth's gravitational field. We show that the underlying mixed phase space of regular skipping motion and random motion due to disorder scattering can be exploited to realize a vectorial velocity filter for ultracold neutrons. The absorbing-reflecting mirror system proposed allows beams of ultracold neutrons with low angular divergence to be formed. The range of velocity components can be controlled by adjusting the geometric parameters of the system. First experimental tests of its performance are presented. One potential future application is the investigation of transport and scattering dynamics in confined systems downstream of the filter.

New methods of flow visualization near absolute zero have opened the way to directly compare quantum turbulence (in superfluid helium) to classical turbulence (in ordinary fluids such as air or water) and explore analogies and differences. We present results of numerical simulations in which we examine the statistics of the superfluid acceleration in thermal counterflow. We find that, unlike the velocity, the acceleration obeys scaling laws similar to classical turbulence, in agreement with a recent quantum turbulence experiment of La Mantia et al.

Electro-osmosis phenomena are studied in a two-dimensional (2D) model disordered porous medium. The flow passages are represented by a network of spatially distributed rectangular channels with random orientations. The channels may represent microfractures in fractured porous media or in a network of interconnected microfractures, pores in a porous medium, or fibers in a fibrous porous material. The linearized equations of electrokinetics are solved numerically in a single channel, and in the 2D network of the channels. The macroscopic electrical conductivity $\sigma$ and electro-osmotic coupling coefficient $\beta$ are computed as functions of the electrical surface potential $\zeta$ and such geometrical parameters of the network as the channels' number density and widths, as well as the porosity of the medium. Despite the complexity of the phenomena and the model of porous media that is used, both $\sigma$ and $\beta$ appear to depend on the characteristics of the phenomena and porous media through very simple relations.

Equilibrium statistical mechanics tools have been developed to obtain indications about the natural tendencies of nonlinear energy transfers in two-dimensional and quasi-two-dimensional flows like rotating and stratified flows in geostrophic balance. In this article we consider a simple model of such flows with a nontrivial vertical structure, namely, two-layer quasigeostrophic flows, which remain amenable to analytical study. We obtain the statistical equilibria of the system in the case of a linear vorticity-stream function relation, build the corresponding phase diagram, and discuss the most probable outcome of nonlinear energy transfers, both on the horizontal and on the vertical, in the presence of stratification and rotation.

A computational method is suggested for the simulation of Liesegang patterns in two dimensions on structureless meshes. The method is based on a model that incorporates dynamical equations for the nucleation and growth of solid particles of different sizes into reaction-diffusion equations. We find the model cannot be numerically solved with Galerkin-based finite element methods and cell-centered finite volume methods. Instead, the vertex-based finite volume method is used to correctly reproduce the Liesegang pattern on structureless meshes. The numerical solution is then compared with specially designed experiments on Liesegang patterns in various geometries, and it is shown to be in good agreement.