We determine the statistics of work in isothermal volume changes of a classical ideal gas consisting of a single particle. Combining our results with the findings of Lua and Grosberg [J. Chem. Phys. B 109, 6805 (2005)] on adiabatic expansions and compressions we then analyze the joint probability distribution of heat and work for a microscopic, nonequilibrium Carnot cycle. In the quasistatic limit we recover Carnot efficiency, however, combined with nontrivial distributions of work and heat. With increasing piston speed the efficiency decreases. The efficiency at maximum power stays within recently derived bounds.

Transport of overdamped Brownian particles in a two-dimensional channel with nonstraight midline and narrow varying width is investigated in the presence of an asymmetric unbiased external force. In the adiabatic limit, we obtain the analytical expression of the directed current. It is found that the current is manipulated by changing the phase shift between the top and bottom walls of the channel. As the phase shift is increased from 0 to $\pi$, the variation of the channel width decreases and the current also decreases. Remarkably, the current is always zero when the phase shift is equal to $\pi$, where the entropic barrier disappears. In addition, the temporal asymmetric parameter of the unbiased force not only determines the direction of the current but also affects its amplitude.

The adaptive Thouless-Anderson-Palmer equation is derived for inverse Ising problems in the presence of quenched random fields. We test the proposed scheme on Sherrington-Kirkpatrick, Hopfield, and random orthogonal models and find that the adaptive Thouless-Anderson-Palmer approach allows accurate inference of quenched random fields whose distribution can be either Gaussian or bimodal. In particular, another competitive method for inferring external fields, namely, the naive mean field method with diagonal weights, is compared and discussed.

We study a planar two-temperature diffusion of a Brownian particle in a parabolic potential. The diffusion process is defined in terms of two Langevin equations with two different effective temperatures in the $X$ and the $Y$ directions. In the stationary regime the system is described by a nontrivial particle position distribution, $P(x,y)$, which we determine explicitly. We show that this distribution corresponds to a nonequilibrium stationary state, characterized by the presence of space-dependent particle currents which exhibit a nonzero rotor. Theoretical results are confirmed by the numerical simulations.

We show that the formation of a gel by conducting colloidal particles leads to a dramatic enhancement in bulk conductivity, due to interparticle electron tunneling, combining predictions from molecular-dynamics simulations with structural measurements in an experimental colloid system. Our results show how colloidal gelation can be used as a general route to huge enhancements of conductivity, and suggest a feasible way for developing cheap materials with novel properties and low metal content.

The stability of nanoparticle suspensions and the details of their agglomeration depend on the interactions between particles. We study this relationship in gold nanoparticles stabilized with different alkyl thiols in heptane. Temperature-dependent interactions were inferred from small-angle x-ray scattering, agglomeration kinetics from dynamic light scattering, and agglomerate morphologies from transmission electron microscopy. We find that the particles precipitate at temperatures below the melting temperatures of the dry ligands. Agglomerates grow with rates that depend on the temperature: Around precipitation temperature, globular agglomerates form slowly, while at lower temperatures, fibrilar agglomerates form rapidly. All agglomerates contain random dense packings rather than crystalline superlattices. We conclude that ligand-ligand and ligand-solvent interactions of the individual particles dominate suspension stability and agglomeration kinetics. The microscopic packing is dominated by interactions between the ligands of different nanoparticles.

A quasielastic neutron scattering (QENS) experiment is a particular technique that endeavors to define a relationship between time and space for the diffusion dynamics of atoms and molecules. However, in most cases, analyses of QENS data are model dependent, which may distort attempts to elucidate the actual diffusion dynamics. We have developed a method for processing QENS data without a specific model, wherein all modes can be described as combinations of the relaxations based on the exponential law. By this method, we can obtain a distribution function $B(Q,\Gamma )$, which we call the mode-distribution function (MDF), to represent the number of relaxation modes and distributions of the relaxation times in the modes. The deduction of MDF is based on the maximum entropy method and is very versatile in QENS data analysis. To verify this method, reproducibility was checked against several analytical models, such as that with a mode of distributed relaxation time, that with two modes closely located, and that represented by the Kohlrausch-Williams-Watts function. We report the first application to experimental data of liquid water. In addition to the two known modes, the existence of a relaxation mode of water molecules with an intermediate time scale has been discovered. We propose that the fast mode might be assigned to an intermolecular motion and the intermediate motion might be assigned to a rotational motion of the water molecules instead of to the fast mode.

We draw several electric-field–temperature ($E$-$T$) phase diagrams with electric-field-induced birefringence contours in the $n$OHFBBB1M7 ($n=10$) and $n$OTBBB1M7 ($n=11$) (C11) mixture system by changing the C11 concentration carefully; some of the mixtures show the unusual extraordinary phase sequence where subphases with the four-, five-, and six-layer superlattice structures emerge above the smectic-$C^{*}$ main phase. We try to understand the results in terms of two complementary models that have so far been proposed: the phenomenological Landau model of phase transitions by Dolganov et al. [P. V. Dolganov et al., Phys. Rev. E 86, 020701(R) (2012)] and the partially molecular Emelyanenko-Osipov model [A. V. Emelyanenko and M. A. Osipov, Phys. Rev. E 68, 051703 (2003)]. The observed $E$-$T$ phase diagram can be well reproduced by the phenomenological model. An emergence of the subphase with the four-layer superlattice structure above smectic-$C^{*}$ is also understandable in terms of the partially molecular model. We discuss the pros and cons of the two models as well.

Based on a coarse-grained model, we carry out molecular dynamics simulations to analyze the diffusion of a small tracer particle inside a cylindrical channel whose inner wall is covered with randomly grafted short polymeric chains. We observe an interesting transient subdiffusive behavior along the cylindrical axis at high attraction between the tracer and the chains, however, the long-time diffusion is always normal. This process is found to be enhanced for the case that we immobilize the grafted chains, i.e., the subdiffusive behavior sets in at an earlier time and spans over a longer time period before becoming diffusive. Even if the grafted chains are replaced with a frozen sea of repulsive, nonconnected particles in the background, a transient subdiffusion is observed. The intermediate subdiffusive behavior only disappears when the grafted chains are replaced with a mobile background sea of mutually repulsive particles. Overall, the long-time diffusion coefficient of the tracer along the cylinder axis decreases with an increase in system volume fraction, the strength of the attraction between the tracer and the background, and also on freezing the background.

Many studies investigating the effect of human social connectivity structures (networks) and human behavioral adaptations on the spread of infectious diseases have assumed either a static connectivity structure or a network which adapts itself in response to the epidemic (adaptive networks). However, human social connections are inherently dynamic or time varying. Furthermore, the spread of many infectious diseases occur on a time scale comparable to the time scale of the evolving network structure. Here we aim to quantify the effect of human behavioral adaptations on the spread of asymptomatic infectious diseases on time varying networks. We perform a full stochastic analysis using a continuous time Markov chain approach for calculating the outbreak probability, mean epidemic duration, epidemic reemergence probability, etc. Additionally, we use mean-field theory for calculating epidemic thresholds. Theoretical predictions are verified using extensive simulations. Our studies have uncovered the existence of an “adaptive threshold,” i.e., when the ratio of susceptibility (or infectivity) rate to recovery rate is below the threshold value, adaptive behavior can prevent the epidemic. However, if it is above the threshold, no amount of behavioral adaptations can prevent the epidemic. Our analyses suggest that the interaction patterns of the infected population play a major role in sustaining the epidemic. Our results have implications on epidemic containment policies, as awareness campaigns and human behavioral responses can be effective only if the interaction levels of the infected populace are kept in check.

Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction spreading, numerical data and analytical estimates show a power-law behavior of the reaction product as $M\left(t\right)\sim t^{d_{\text{l}}}$, where $d_{\text{l}}$ is the connectivity dimension. In a percolating channel, a statistically stationary traveling wave develops. The speed and the width of the traveling wave are numerically computed. While the front speed is a low-fluctuating quantity and its behavior can be understood using a simple theoretical argument, the front width is a high-fluctuating quantity showing a power-law behavior as a function of the size of the channel.

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean-field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.

We present a numerical study of the pulses displayed by a semiconductor laser with optical feedback in the short-cavity regime, such that the external cavity round-trip time is shorter than the laser relaxation oscillation period. For certain parameters there are occasional pulses, which are high enough to be considered extreme events. We characterize the bifurcation scenario that gives rise to such extreme pulses and study the influence of noise. We demonstrate intermittency when the extreme pulses appear and hysteresis when the attractor that sustains these pulses is destroyed. We also show that this scenario is robust under the inclusion of noise.

We explore the fundamental question of the critical nonlinearity value needed to dynamically localize energy in discrete nonlinear cubic (Kerr) lattices. We focus on the effective frequency and participation ratio of the profile to determine the transition into localization in one-, two-, and three-dimensional lattices. A simple and general criterion is developed, for the case of an initially localized excitation, to define the transition region in parameter space (“dynamical tongue”) from a delocalized to a localized profile. We introduce a method for computing the dynamically excited frequencies, which helps us validate our stationary ansatz approach and the effective frequency concept. A general analytical estimate of the critical nonlinearity is obtained, with an extra parameter to be determined. We find this parameter to be almost constant for two-dimensional systems and prove its validity by applying it successfully to two-dimensional binary lattices.

The effects of purely elastic collisions on the dynamics of heavy inertial particles are investigated in a three-dimensional random incompressible flow. It is shown that the statistical properties of interparticle separations and relative velocities are strongly influenced by the occurrence of sticky elastic collisions—particle pairs undergo a large number of collisions against each other during a small time interval over which, hence, they remain close to each other. A theoretical framework is provided for describing and quantifying this phenomenon and it is substantiated by numerical simulations. Furthermore, the impact of hydrodynamic interactions is discussed for such a system of colliding particles.

A mapping of avalanches occurring in the zero-temperature random-field Ising model to life periods of a population experiencing immigration is established. Such a mapping allows the microscopic criteria for the occurrence of an infinite avalanche in a $q$-regular graph to be determined. A key factor for an avalanche of spin flips to become infinite is that it interacts in an optimal way with previously flipped spins. Based on these criteria, we explain why an infinite avalanche can occur in $q$-regular graphs only for $q>3$ and suggest that this criterion might be relevant for other systems. The generating function techniques developed for branching processes are applied to obtain analytical expressions for the durations, pulse shapes, and power spectra of the avalanches. The results show that only very long avalanches exhibit a significant degree of universality.

We propose a collective opinion formation model with a so-called confirmation bias. The confirmation bias is a psychological effect with which, in the context of opinion formation, an individual in favor of an opinion is prone to misperceive new incoming information as supporting the current belief of the individual. Our model modifies a Bayesian decision-making model for single individuals [M. Rabin and J. L. Schrag, Q. J. Econ. 114, 37 (1999)] for the case of a well-mixed population of interacting individuals in the absence of the external input. We numerically simulate the model to show that all the agents eventually agree on one of the two opinions only when the confirmation bias is weak. Otherwise, the stochastic population dynamics ends up creating a disagreement configuration (also called polarization), particularly for large system sizes. A strong confirmation bias allows various final disagreement configurations with different fractions of the individuals in favor of the opposite opinions.

This paper studies the Katz-Lebowitz-Spohn (KLS) process on lattices with a junction, where particles move on parallel lattice branches that combine into a single lattice at the junction. It is shown that 11 kinds of phase diagrams could be observed, depending on the two parameters $\epsilon$ and $\delta$ in the KLS process. We have investigated the phase diagrams as well as bulk density analytically based on flow rate conservation and the extremal current principle. Extensive Monte Carlo computer simulations are performed, and it is found that they are in excellent agreement with theoretical prediction.

Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed “universe.” A question remains with regard to what the minimally required description for the surrounding of such an open driven system is so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system or in a quasisteady state (QSS) with an excess amount of adenosine triphosphate (ATP), adenosine diphosphate (ADP), and inorganic phosphate (Pi). We introduce the key notion of minimal work that is needed, $W_{\min }$, for the external regenerating system to sustain a NESS (e.g., maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the second law in terms of the same positive entropy production rate. The heat dissipation of a NESS without mechanical output is exactly the $W_{\min }$. This provides a justification for introducing an ideal external regenerating system and yields a free-energy balance equation between the net free-energy input $F_{\mathrm{in}}$ and total dissipation $F_{\mathrm{dis}}$ in an NESS: $F_{\mathrm{in}}$ consists of chemical input minus mechanical output; $F_{\mathrm{dis}}$ consists of dissipative heat, i.e. the amount of useful energy becoming heat, which also equals the NESS entropy production. Furthermore, we show that for nonstationary systems, the $F_{\mathrm{dis}}$ and $F_{\mathrm{in}}$ correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics and identify a relative entropy $H$ as a generalized free energy. We reach a new formulation of Markovian nonequilibrium thermodynamics based on only the internal kinetic equation without further reference to the intrinsic degree of freedom within each Markov state. It includes an extended free-energy balance and a second law which are valid for driven stochastic dynamics with an ideal external regenerating system. Our result suggests new ingredients for a generalized thermodynamics of self-organization in driven systems.

The liquid-liquid phase transition (LLPT) in aqueous salt solutions of lysozyme protein has been studied by small-angle neutron scattering. Measurements have been carried out on fixed protein concentration with varying salt concentration approaching LLPT. The data are fitted considering protein interaction by the two Yukawa (2Y) potential which combines short-range attraction and long-range repulsion. We show that LLPT arises because of enhancement of non-DLVO (Derjaguin-Landau-Verwey-Overbeek) short-range attraction without any conformational structural change of the protein. The salt concentration required for LLPT as well as corresponding short-range attraction decreases significantly with increase in protein concentration.