The eigenstate thermalization hypothesis (ETH) implies a form for the matrix elements of local operators between eigenstates of the Hamiltonian, expected to be valid for chaotic systems. Another signal of chaos is a positive Lyapunov exponent, defined on the basis of Loschmidt echo or out of time order correlators. For this exponent to be positive, correlations between matrix elements unrelated by symmetry, usually neglected, have to exist. The same is true for the peak of the dynamic heterogeneity length ${\chi }_4$, relevant for systems with slow dynamics. These correlations, as well as those between elements of different operators, are encompassed in a generalized form of ETH.

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous degradation process. The seminal model of that kind leads to gamma distributions of protein levels, whose parameters are defined by the mean frequency of protein bursts and mean burst size. However, such models (whether interpreted in terms of molecule numbers or concentrations) do not correctly account for the noise due to protein partitioning between daughter cells. We present an exactly solvable stochastic model of gene expression in cells dividing at random times, where we assume description in terms of molecule numbers with a constant mean protein burst size. The model is based on a population balance equation supplemented with protein production in random bursts. If protein molecules are partitioned equally between daughter cells, we obtain at steady state the analytical expressions for probability distributions similar in shape to gamma distributions, yet with quite different values of mean burst size and mean burst frequency than would result from fitting of the classical continuous-decay model to these distributions. For random partitioning of protein molecules between daughter cells, we obtain the moment equations for the protein number distribution and thus the analytical formulas for the squared coefficient of variation.

This paper studies numerically the collapse of a cluster of cavitation bubbles (as a primitive model for a bubble cloud) near a solid wall. The homogeneous two-phase mixture model is used, with the liquid-vapor interface resolved by volume of fluid method. The liquid is treated as compressible, allowing the propagation of pressure waves at the speeds determined by a state equation. This cluster consists of 27 identical bubbles, evenly distributed in a cubic region, with various bubble-wall and bubble-bubble distances considered. Our simulations suggest that the bubble-wall distance plays a more significant role. The maximum impulsive pressure of $41\mathrm{MPa}$ is achieved when the cluster is very close to the wall. The inward progress of collapse is observed by examining the evolutions of bubble shapes and flow fields, with two distinctly different sequences of collapse identified between the small and large bubble-wall distances. At a large bubble distance, the centermost bubble is the last to collapse, while at a small bubble distance, it is the central bubble nearest to the wall which collapses lastly. This difference can also explain the more intensive impulsive pressure for the smaller bubble-wall distances. The proposed numerical approach is of special interest because it can resolve the details of bubble-bubble and bubble-wall interactions, which are significant to the study of the collapse of a cavitation cloud, and its potential damage to hydraulic systems.

Thanks to the development of machine learning techniques, it has been shown that the supervised learning can be useful to study critical phenomena of various systems. However, the supervised learning cannot be done without labels which require knowledge about critical behavior of the system. To overcome this barrier, unsupervised machine learning methods have been considered and the confusion scheme has been proposed. In this study, we use the confusion scheme of the unsupervised learning and investigate critical behavior of various systems which exhibit single (double) phase transitions with (without) quasi-long-range order. In detail, we choose the two-color Ashkin-Teller model, the $XY$ model, and the eight-state clock model as such systems and snapshots of the spin configurations at various temperatures are collected via Monte Carlo simulations to be used as input data for the unsupervised machine learning. We also put focus on the size dependence of results and validate the availability of the confusion scheme in thermodynamic limit. Our results indicate that the confusion scheme of the unsupervised learning successfully locates the approximate transition points for all models and becomes more accurate as the system size is increased. We also find a characteristic feature of the result which reflects the presence of a quasi-long-range order. We conclude that regardless of the presence of a quasi-long-range order, single and double phase transitions can be detected via the confusion scheme.

Dharma-wardana et al. [M. W. C. Dharma-wardana et al., Phys. Rev. E 96, 053206 (2017)] recently calculated dynamic electrical conductivities for warm dense matter as well as for nonequilibrium two-temperature states termed “ultrafast matter” (UFM) [M. W. C. Dharma-wardana, Phys. Rev. E 93, 063205 (2016)]. In this Comment we present two evident reasons why these UFM calculations are neither suited to calculate dynamic conductivities nor x-ray Thomson scattering spectra in isochorically heated warm dense aluminum. First, the ion-ion structure factor, a major input into the conductivity and scattering spectra calculations, deviates strongly from that of isochorically heated aluminum. Second, the dynamic conductivity does not show a non-Drude behavior which is an essential prerequisite for a correct description of the absorption behavior in aluminum. Additionally, we clarify misinterpretations by Dharma-wardana et al. concerning the conductivity measurements of Gathers [G. R. Gathers, Int. J. Thermophys. 4, 209 (1983)].

We present a model for an autonomous quantum thermal machine composed of two qubits capable of manipulating and even amplifying the local coherence in a nondegenerate external system. The machine uses only thermal resources, namely, contact with two heat baths at different temperatures, and the external system has a nonzero initial amount of coherence. The method we propose allows for an interconversion between energy, both work and heat, and coherence in an autonomous configuration working in out-of-equilibrium conditions. This model raises interesting questions about the role of fundamental limitations on transformations involving coherence and opens up new possibilities in the manipulation of coherence by autonomous thermal machines.

We study the problem of identifying macroscopic structures in networks, characterizing the impact of introducing link directions on the detectability phase transition. To this end, building on the stochastic block model, we construct a class of nontrivially detectable directed networks. We find closed-form solutions by using the belief propagation method, showing how the transition line depends on the assortativity and the asymmetry of the network. Finally, we numerically identify the existence of a hard phase for detection close to the transition point.

A numerical method for modeling and understanding the dynamics of bubble oscillations subjected to fast variations in the ambient pressure is proposed under low Mach number conditions. In the present work, the method uses a single-fluid continuum formalism of weakly compressible axisymmetric Navier-Stokes equations for the numerical simulation of liquid-gas flows with surface tension and adopts the interface capturing approach based on a coupled level set and volume of fluid (CLSVOF) method for describing the moving and deformed interfaces. To demonstrate the efficacy of the proposed method, first, the numerical results of the radial oscillations of a spherical gas bubble are tested with the numerical solutions of Rayleigh-Plesset equation. Then, the numerical method is applied to reproduce the growth and subsequent collapse of a bubble in an infinite liquid medium observed in experiments. Finally, the numerical simulation of the interaction of two oscillating bubbles at small separation distance is evaluated in response to a moderate step change in the ambient pressure. It is shown that two deformable bubbles undergo coupled radial and oscillatory translational motions which eventually results in the bubbles' attraction and coalescence caused by the secondary Bjerknes forces. The numerical predictions show very good accuracy with the experimental and numerical results reported in the literature.

Electric forcing can be used to select and to regulate the shape of liquid metals. In this work, we present a transition among different patterns in a liquid mercury drop regulated by noise. A stochastic resonancelike phenomenon was observed for two different structural transitions of the liquid metal. In the first set of experiments, the transition from irregular (I) $\to$ triangular (T) $\to$ irregular (I) patterns was obtained by increasing the amplitude of biased white noise. In the second part, we observed the transition from irregular (I) $\to$ elliptical (E) $\to$ irregular (I) patterns using the same kind of noise. Periodic stochastic resonance was corroborated in our experiments by employing the cross-correlation coefficient technique.

We consider a stochastic interface $h(x,t)$, described by the $1+1$ Kardar-Parisi-Zhang (KPZ) equation on the half line $x\ge 0$ with the reflecting boundary at $x=0$. The interface is initially flat, $h(x,t=0)=0$. We focus on the short-time probability distribution $\mathcal{P}(H,L,t)$ of the height $H$ of the interface at point $x=L$. Using the optimal fluctuation method, we determine the (Gaussian) body of the distribution and the strongly asymmetric non-Gaussian tails. We find that the slower-decaying tail scales as $-\sqrt{t}ln\mathcal{P}\simeq {\left|H\right|}^{3/2}{f}_{-}(L/\sqrt{\left|H\right|t})$ and calculate the function $f_{-}$ analytically. Remarkably, this tail exhibits a first-order dynamical phase transition at a critical value of $L$, $L_c=0.60223\cdots \sqrt{\left|H\right|t}$. The transition results from a competition between two different fluctuation paths of the system. The faster-decaying tail scales as $-\sqrt{t}ln\mathcal{P}\simeq {\left|H\right|}^{5/2}{f}_{+}(L/\sqrt{\left|H\right|t})$. We evaluate the function $f_{+}$ using a specially developed numerical method which involves solving a nonlinear second-order elliptic equation in Lagrangian coordinates. The faster-decaying tail also involves a sharp transition which occurs at a critical value $L_c\simeq 2\sqrt{2\left|H\right|t}/\pi$. This transition is similar to the one recently found for the KPZ equation on a ring, and we believe that it has the same fractional order, $5/2$. It is smoothed, however, by small diffusion effects.

In the self-assembly process which drives the formation of cellular membranes, micelles, and capsids, a collection of separated subunits spontaneously binds together to form functional and more ordered structures. In this work, we study the statistical physics of self-assembly in a simpler scenario: the formation of dimers from a system of monomers. The properties of the model allow us to frame the microstate counting as a combinatorial problem whose solution leads to an exact partition function. From the associated equilibrium conditions, we find that such dimer systems come in two types: ”search-limited” and ”combinatorics-limited,” only the former of which has states where partial assembly can be dominated by correct contacts. Using estimates of biophysical quantities in systems of single-stranded DNA dimerization, transcription factor and DNA interactions, and protein-protein interactions, we find that all of these systems appear to be of the search-limited type, i.e., their fully correct dimerization regimes are more limited by the ability of monomers to find one another in the constituent volume than by the combinatorial disadvantage of correct dimers. We derive the parameter requirements for fully correct dimerization and find that rather than the ratio of particle number and volume (i.e., number density) being the relevant quantity, it is the product of particle diversity and volume that is constrained. Ultimately, this work contributes to an understanding of self-assembly by using the simple case of a system of dimers to analytically study the combinatorics of assembly.

Directed percolation (DP) is a classic model for nonequilibrium phase transitions into a single absorbing state ($fixation$). It has been extensively studied by analytical and numerical techniques in diverse contexts. Recently, DP has appeared as a generic model for the evolutionary and ecological dynamics of competing bacterial populations. Range expansion—the stochastic reproduction of bacteria competing for space to be occupied by their progeny—leads to a fluctuating and rough growth front, which is known from experiment and simulation to affect the underlying critical behavior of the DP transition. In this work, we employ symmetry arguments to construct a pair of nonlinear stochastic partial differential equations describing the coevolution of surface roughness with the composition field of DP. Macroscopic manifestations (phenomenology) of these equations on growth patterns and genealogical tracks of range expansion are discussed; followed by a renormalization group analysis of possible scaling behaviors at the DP transition.

By means of studying the evolution equation for the Wigner distributions of quantum dissipative systems we derive the quantum corrections to the classical Liouville dynamics, taking into account the standard quantum friction model. The resulting evolution turns out to be the classical one plus fluctuations that depend not only on the $\hslash$ size but also on the momentum and the dissipation parameter (i.e., the coupling with the environment). On the other hand, we extend our studies of a paradigmatic system based on the kicked rotator, and we confirm that by adding fluctuations only depending on the size of the Planck constant we essentially recover the quantum behavior. This is systematically measured in the parameter space with the overlaps and differences in the dispersion of the marginal distributions corresponding to the Wigner functions. Taking into account these results and analyzing the Wigner evolution equation we conjecture that the chaotic nature of our system is responsible for the independence on the momentum, while the dependence on the dissipation is provided implicitly by the dynamics.

The mechanics of disordered fibrous networks such as those that make up the extracellular matrix are strongly dependent on the local connectivity or coordination number. For biopolymer networks this coordination number is typically between 3 and 4. Such networks are sub-isostatic and linearly unstable to deformation with only central force interactions, but exhibit a mechanical phase transition between floppy and rigid states under strain. The introduction of weak bending interactions stabilizes these networks and suppresses the critical signatures of this transition. We show that applying external stress can also stabilize subisostatic networks with only tensile central force interactions, i.e., a ropelike potential. Moreover, we find that the linear shear modulus shows a power-law scaling with the external normal stress, with a non-mean-field exponent. For networks with finite bending rigidity, we find that the critical stain shifts to lower values under prestress.

Using a population dynamics inspired by an ensemble of growing cells, a set of fluctuation theorems linking observables measured at the lineage and population levels is derived. One of these relations implies specific inequalities comparing the population doubling time with the mean generation time at the lineage or population levels. While these inequalities have been derived before for age-controlled models with negligible mother-daughter correlations, we show that they also hold for a broad class of size-controlled models. We discuss the implications of this result for the interpretation of a recent experiment in which the growth of bacteria strains has been probed at the single-cell level.

Intermediate filaments are long elastic fibers that are transported by the microtubule-associated motor proteins kinesin and dynein inside the cell. How elastic filaments are efficiently transported by antagonistic motors is not well understood and is difficult to measure with current experimental techniques. Adapting the tug-of-war paradigm for vesiclelike cargos, we develop a mathematical model to describe the motion of an elastic filament punctually bound to antagonistic motors. As observed in cells, up to three modes of transport are obtained; dynein-driven retrograde, kinesin-driven anterograde fast motions, and a slow motion. Motor properties and initial conditions that depend on intracellular context regulate the transport of filaments. Filament elasticity is found to affect both the mode and the efficiency of transport. We further show that the coordination of motors along the filament emerges from the interplay between intracellular context and elastic properties of filaments.

Population dynamics deals with the collective phenomena of living organisms, and it has attracted much attention since it is expected to explain how not only living organisms but also human beings have been adapted to varying environments. However, it is quite difficult to insist on a general statement on living organisms since mathematical models heavily depend on phenomena that we focus on. Recently, it was reported that the fluctuation relations on the fitness of living organisms held for a quite general problem setting. But, interactions between organisms were not incorporated in the problem setting, though interaction plays critical roles in collective phenomena in physics and population dynamics. In this paper, we propose interacting models for population dynamics and provide the perturbative theory of population dynamics. Then, we derive the variational principle and fluctuation relations for interacting population dynamics.

Unsupervised learning as an important branch of machine learning is commonly adopted to discover patterns, with the purpose of conducting data clustering without being labeled in advance. In this study, we elucidate the striking ability of unsupervised learning techniques in exploring the phase transitions of polymer configurations. In order to extract the low-dimensional representation of polymer configurations, principal component analysis and diffusion map are applied to distinguish the coiled state and collapsed states and further detect the delicate distinction among collapsed states, respectively. These dimensionality reduction techniques not only identify the distinct states in the feature space, but also offer significant insights to understand the relation between salient features and order parameters in physics. In addition, a hybrid neural network scheme combining the supervised learning and unsupervised learning is utilized to precisely detect the critical point of phase transition between polymer configurations. Our study demonstrates a promising strategy based on the unsupervised learning, particularly in the exploration of phase transition in polymeric systems.

We consider the formalism of information decomposition of target effects from multisource interactions, i.e., the problem of defining redundant and synergistic components of the information that a set of source variables provides about a target, and apply it to the two-dimensional Ising model as a paradigm of a critically transitioning system. Intuitively, synergy is the information about the target variable that is uniquely obtained by taking the sources together, but not considering them alone; redundancy is the information which is shared by the sources. To disentangle the components of the information both at the static level and at the dynamical one, the decomposition is applied respectively to the mutual information and to the transfer entropy between a given spin, target, and a pair of neighboring spins (taken as the drivers). We show that a key signature of an impending phase transition (approached from the disordered size) is the fact that the synergy peaks in the disordered phase, both in the static and in the dynamic case: The synergy can thus be considered a precursor of the transition. The redundancy, instead, reaches its maximum at the critical temperature. The peak of the synergy of the transfer entropy is far more pronounced than those of the static mutual information. We show that these results are robust with respect to the details of the information decomposition approach, as we find the same results using two different methods; moreover, with respect to previous literature rooted in the notion of global transfer entropy, our results demonstrate that considering as few as three variables is sufficient to construct a precursor of the transition, and provide a paradigm for the investigation of a variety of systems prone to crisis, such as financial markets, social media, or epileptic seizures.

Momentum accommodation is a key factor governing the transport of particles in gases from electric mobility and Brownian diffusion to thermophoresis. This paper explores the relationship between momentum accommodation of nanoparticles in dilute gases and surface adsorption. We demonstrate that the momentum accommodation factor is fundamentally equal to the probability of surface adsorption. Molecular dynamics simulations show that surface adsorption is the key mechanism behind the diffuse scattering model, and that upon gas-particle collision the immediate reflection dynamics and surface adsorption events are governed by the kinetic energy distribution of the rebounding gas molecules. This distribution determines the transition of the dominant mode of molecular scattering off a particle surface from diffuse to specular elastic reflection as the particle approaches the realm of molecular size. The kinetics and equilibrium of physisorption are examined to shed light on the effect of the lifetime of surface adsorbates on momentum transfer. A statistical treatment is proposed for the adsorption and hence the gas-nanoparticle momentum accommodation coefficient. The validity of the theoretical treatment is examined by comparing its prediction against experimental mobility data of silver nanoparticles.