The strong connection between correlations and quantum thermodynamics raises a natural question about the preparation of correlated quantum states from two copies of a thermal qubit. In this work we study the specific forms of allowed and forbidden bipartite correlations. As a consequence, we extend the result to separable but not absolutely separable class of product states. Preparation of a general form of entanglement from arbitrary thermal qubits is studied and, as an application, we propose a strategy to establish desired entanglement between two distant parties. The threshold temperature to produce entanglement from two copies of a thermal qubit has also been discussed from the resource theoretic perspective, which ensures that the bound on the temperature can be superseded with the help of a resource state. A dimension dependent upper bound on the temperature is derived, below which two copies of any $d$-dimensional thermal state can be entangled in $2\times d$ dimensions.

The second law of thermodynamics holds that the efficiency of heat engines, classical or quantum, cannot be greater than the universal Carnot efficiency. We discover another bound for the efficiency of a quantum Otto heat engine consisting of a harmonic oscillator. Dynamics of the engine is governed by the Lindblad equation for the density matrix, which is mapped to the Fokker-Planck equation for the quasiprobability distribution. Applying stochastic thermodynamics to the Fokker-Planck equation system, we obtain the $\hslash$-dependent quantum mechanical bound for the efficiency. It turns out that the bound is tighter than the Carnot efficiency. The engine achieves the bound in the low-temperature limit where quantum effects dominate. Our work demonstrates that quantum nature could suppress the performance of heat engines in terms of efficiency bound, work, and power output.

Chimera states have been a vibrant subject of research in the recent past, but the analytical treatment of transitions from chimeras to coherent states remains a challenge. Here we analytically derive the necessary conditions for this transition by means of the coherent stability function approach, which is akin to the master stability function approach that is traditionally used to study the stability of synchronization in coupled oscillators. In chimera states, there is typically at least one group of oscillators that evolves in a drifting, random manner, while other groups of oscillators follow a smoother, more coherent profile. In the coherent state, there thus exists a smooth functional relationship between the oscillators. This lays the foundation for the coherent stability function approach, where we determine the stability of the coherent state. We subsequently test the analytical prediction numerically by calculating the strength of incoherence during the transition point. We use leech neurons, which exhibit a coexistence of chaotic and periodic tonic spiking depending on initial conditions, coupled via nonlocal electrical synapses, to demonstrate our approach. We systematically explore various dynamical states with the focus on the transitions between chimeras and coherence, fully confirming the validity of the coherent stability function. We also observe complete synchronization for higher values of the coupling strength, which we verify by the master stability function approach.

Using Monte Carlo numerical simulation, this work sketches the phase diagram of systems of certain hard $C_{2h}$-symmetric particles, formed by gluing two aligned and displaced hard spherocylinders with a cylindrical-length-to-diameter ratio realistically, if viewed not only from the lyotropic colloidal liquid-crystal side but also from the thermotropic low-molecular-mass liquid-crystal side, equal to 5, as a function of the displacement. Several distinctive phases are observed, such as a nonperiodic smectic-B-like phase, a nonperiodic smectic-$H$-like phase, a smectic-$C$ phase, and a short-layer-spacing uniaxial smectic-A phase but no biaxial nematic phase.

The Landau theory of phase transitions has been productively applied to phase transitions that involve rotational symmetry breaking, such as the transition from an isotropic fluid to a nematic liquid crystal. It even can be applied to the orientational symmetry breaking of simple atomic or molecular clusters that are not true phase transitions. In this paper, we address fundamental problems that arise with the Landau theory when it is applied to rotational symmetry breaking transitions of more complex particle clusters that involve order parameters characterized by larger values of the $l$ index of the dominant spherical harmonic that describes the broken symmetry state. The problems are twofold. First, one may encounter a thermodynamic instability of the expected ground state with respect to states with lower symmetry. A second problem concerns the proliferation of quartic invariants that may or may not be physical. We show that the combination of a geometrical method based on the analysis of the space of invariants, developed by Kim to study symmetry breaking of the Higgs potential, with modern visualization tools provides a resolution to these problems. The approach is applied to the outcome of numerical simulations of particle ordering on a spherical surface and to the ordering of protein shells.

Solar systems complexity, multiscale, and nonlinearity are governed by numerous and continuous changes where the sun magnetic fields can successfully represent many of these phenomena. Thus, nonlinear tools to study these challenging systems are required. The dynamic system recurrence approach has been successfully used to deal with this kind challenge in many scientific areas, objectively improving the recognition of state changes, randomness, and degrees of complexity that are not easily identified by traditional techniques. In this work we introduce the use of these techniques in photospheric magnetogram series. We employ a combination of recurrence quantification analysis with a preprocessing denoising wavelet analysis to characterize the complexity of the magnetic flux emergence in the solar photosphere. In particular, with the developed approach, we identify regions of evolving magnetic flux and where they present a large degree of complexity, i.e., where predictability is low, intermittence is high, and low organization is present.

We investigate a range of rule-based models of the in-plane structure of growing single-cell-thick epithelia represented by the distribution of frequencies of polygon classes. Within the Markovian framework introduced by Gibson et al. [Nature (London) 442, 1038 (2006)], we discuss various topologically allowed cell division schemes assumed to control the structure of the tissue as well as a phenomenological Gaussian scheme, and we compute the stationary distributions for all of them. Some of the distributions reproduce those seen in tissues characterized by unbiased mitotic events but also in certain tissues with a preferred orientation of the mitotic plane or a cell-rearrangement process such as neighbor exchange. In addition, we propose the asynchronous-division variant of the model, which builds on the Lewis law and on the Aboav-Weaire law as well as on the fact that the dividing cells are larger than the resting cells. This generalization a posteriori validates the original model.

Monte Carlo simulations are used to study the translocation of a polymer into a cavity. Modeling the polymer as a hard-sphere chain with a length up to $N=601$ monomers, we use a multiple-histogram method to measure the variation of the conformational free energy of the polymer with respect to the number of translocated monomers. The resulting free-energy functions are then used to obtain the confinement free energy for the translocated portion of the polymer. We characterize the confinement free energy for a flexible polymer in cavities with constant cross-sectional area $A$ for various cavity shapes (cylindrical, rectangular, and triangular) as well as for tapered cavities with pyramidal and conical shape. The scaling of the free energy with cavity volume and translocated polymer subchain length is generally consistent with predictions from simple scaling arguments, with small deviations in the scaling exponents likely due to finite-size effects. The confinement free energy depends strongly on cavity shape anisometry and is a minimum for an isometric cavity shape with a length-to-width ratio of unity. Entropic depletion at the edges or vertices of the confining cavity are evident in the results for constant-$A$ and pyramidal cavities. For translocation into infinitely long cones, the scaling of the free energy with taper angle is consistent with a theoretical prediction employing the blob model. We also examine the effects of polymer bending rigidity on the translocation free energy for cylindrical cavities. For isometric cavities, the observed scaling behavior is in partial agreement with theoretical predictions, with discrepancies arising from finite-size effects that prevent the emergence of well-defined scaling regimes. In addition, translocation into highly anisometric cylindrical cavities leads to a multistage folding process for stiff polymers. Finally, we examine the effects of crowding agents inside the cavity. We find that the confinement free energy increases with crowder density. At constant packing fraction the magnitude of this effect lessens with increasing crowder size for a crowder-to-monomer size ratio $\ge 1$.

The viscous coarsening of a phase separated mixture is studied and the effects of the viscosity contrast between the phases are investigated. From an analysis of the microstructure, it appears that for moderate departure from the perfectly symmetric regime the self-similar bicontinuous regime is robust. However, the connectivity of one phase decreases when its volume fraction decreases or when it is becoming less viscous than the complementary phase. Eventually self-similarity breakdown is observed and characterized.

We present a numerical study of a two-lane version of the stochastic nonequilibrium model known as the totally asymmetric simple exclusion process. For such a system with open boundaries, and suitably chosen values of externally imposed particle injection ($\alpha$) and ejection ($\beta$) rates, spontaneous symmetry breaking can occur. We investigate the statistics and internal structure of the stochastically induced transitions or “flips,” which occur between opposite broken-symmetry states as the system evolves in time. From the distribution of time intervals separating successive flips, we show that the evolution of the associated characteristic times against externally imposed rates yields information regarding the proximity to a critical point in parameter space. On short timescales, we probe for the possible existence of precursor events to a flip between opposite broken-symmetry states. We study an adaptation of domain-wall theory to mimic the density reversal process associated with a flip.

We study normal diffusive and subdiffusive processes in a harmonic potential (Ornstein-Uhlenbeck process) on a uniformly growing or contracting domain. Our starting point is a recently derived fractional Fokker-Planck equation, which covers both the case of Brownian diffusion and the case of a subdiffusive continuous-time random walk (CTRW). We find a high sensitivity of the random walk properties to the details of the domain growth rate, which gives rise to a variety of regimes with extremely different behaviors. At the origin of this rich phenomenology is the fact that the walkers still move while they wait to jump, since they are dragged by the deterministic drift arising from the domain growth. Thus, the increasingly long waiting times associated with the aging of the subdiffusive CTRW imply that, in the time interval between two consecutive jumps, the walkers might travel over much longer distances than in the normal diffusive case. This gives rise to seemingly counterintuitive effects. For example, on a static domain, both Brownian diffusion and subdiffusive CTRWs yield a stationary particle distribution with finite width when a harmonic potential is at play, thus indicating a confinement of the diffusing particle. However, for a sufficiently fast growing or contracting domain, this qualitative behavior breaks down, and differences between the Brownian case and the subdiffusive case are found. In the case of Brownian particles, a sufficiently fast exponential domain growth is needed to break the confinement induced by the harmonic force; in contrast, for subdiffusive particles such a breakdown may already take place for a sufficiently fast power-law domain growth. Our analytic and numerical results for both types of diffusion are fully confirmed by random walk simulations.

We consider a model of power distribution in a social system where a set of agents plays a simple game on a graph: The probability of winning each round is proportional to the agent's current power, and the winner gets more power as a result. We show that when the agents are distributed on simple one-dimensional and two-dimensional networks, inequality grows naturally up to a certain stationary value characterized by a clear division between a higher and a lower class of agents. High class agents are separated by one or several lower class agents which serve as a geometrical barrier preventing further flow of power between them. Moreover, we consider the effect of redistributive mechanisms, such as proportional (nonprogressive) taxation. Sufficient taxation will induce a sharp transition towards a more equal society, and we argue that the critical taxation level is uniquely determined by the system geometry. Interestingly, we find that the roughness and Shannon entropy of the power distributions are a very useful complement to the standard measures of inequality, such as the Gini index and the Lorenz curve.

Motivated by the effect of electroautocatalysis (explicit concentration dependence) on the stability of electrochemically driven phase-separating single particles, we apply the Fokker-Planck equation to describe the population dynamics of a general ensemble of chemically reactive particles. For phase-separating ensembles, we show that mosaic instability (from a homogeneous initial state to a multimodal probability distribution) may be suppressed or enhanced by autoinhibitory or autocatalytic reactions, respectively. In some cases, autocatalysis may induce two distinct populations in thermodynamically stable single-phase ensembles. Asymmetric reaction kinetics also results in qualitatively different population dynamics upon reversing the reaction direction. In the limit of negligible fluctuations, we use the method of characteristics and linearization to study the evolution of the concentration variance as well as the condition for mosaic instability, in good agreement with the full numerical solution. Applications include Li-ion batteries characterized by in situ x-ray diffraction.

The quantum dynamics of isolated systems under quench condition exhibits a variety of interesting features depending on the integrable/chaotic nature of system. We study the exact dynamics of trivially integrable system of harmonic chains under a multiple quench protocol. Out of time ordered correlator of two Hermitian operators at large time displays scrambling in the thermodynamic limit. In this limit, the entanglement entropy and the central component of momentum distribution both saturate to a steady-state value. We also show that reduced density matrix assumes the diagonal form long after multiple quenches for large system size. These exact results involving infinite-dimensional Hilbert space are indicative of dynamical equilibration for a trivially integrable harmonic chain.

Using a delay differential equation model we study theoretically the dynamics of a unidirectional class-$A$ ring laser with a nonlinear amplifying loop mirror. We perform linear stability analysis of the continuous-wave regimes in the large delay limit and demonstrate that these regimes can be destabilized via modulational and Turing-type instabilities, as well as by an instability leading to the appearance of square-waves. We investigate the formation of square waves and mode-locked pulses in the system. We show that mode-locked pulses are asymmetric with exponential decay of the trailing edge in positive time and faster-than-exponential (superexponential) decay of the leading edge in negative time. We discuss asymmetric interaction of these pulses leading to a formation of harmonic mode-locked regimes.

The spectrum of the adjacency matrix plays several important roles in the mathematical theory of networks and network data analysis, for example in percolation theory, community detection, centrality measures, and the theory of dynamical systems on networks. A number of methods have been developed for the analytic computation of network spectra, but they typically assume that networks are locally treelike, meaning that the local neighborhood of any node takes the form of a tree, free of short loops. Empirically observed networks, by contrast, often have many short loops. Here we develop an approach for calculating the spectra of networks with short loops using a message passing method. We give example applications to some previously studied classes of networks and find that the presence of loops induces substantial qualitative changes in the shape of network spectra, generating asymmetries, multiple spectral bands, and other features.

Stick-slip motion, a common phenomenon observed during crawling of cells, is found to be strongly sensitive to the substrate stiffness. Stick-slip behaviors have previously been investigated typically using purely elastic substrates. For a more realistic understanding of this phenomenon, we propose a theoretical model to study the dynamics on a viscoelastic substrate. Our model, based on a reaction-diffusion framework, incorporates known important interactions such as retrograde flow of actin, myosin contractility, force-dependent assembly, and disassembly of focal adhesions coupled with cell-substrate interaction. We show that consideration of a viscoelastic substrate not only captures the usually observed stick-slip jumps but also predicts the existence of an optimal substrate viscosity corresponding to maximum traction force and minimum retrograde flow which was hitherto unexplored. Moreover, our theory predicts the time evolution of individual bond force that characterizes the stick-slip patterns on soft versus stiff substrates. Our analysis also elucidates how the duration of the stick-slip cycles are affected by various cellular parameters.

We prove that the plane Couette and Poiseuille flows are nonlinearly stable if the Reynolds number is less than ${\mathrm{Re}}_{\mathrm{Orr}}(2\pi /(\lambda sin\theta ))/sin\theta$ when a perturbation is a tilted perturbation in the direction $x^{\prime }$ which forms an angle $\theta \in (0,\pi /2]$ with the direction $\mathbf{i}$ of the basic motion and does not depend on $x^{\prime }$. ${\mathrm{Re}}_{\mathrm{Orr}}$ is the critical Orr-Reynolds number for spanwise perturbations which is computed for wave number $2\pi /(\lambda sin\theta )$, with $\lambda$ being any positive wavelength. By taking the minimum with respect to $\lambda$, we obtain the critical energy Reynolds number for a fixed inclination angle and any wavelength: for plane Couette flow, it is ${\mathrm{Re}}_{\mathrm{Orr}}=44.3/sin\theta$, and for plane Poiseuille flow, it is ${\mathrm{Re}}_{\mathrm{Orr}}=87.6/sin\theta$ (in particular, for $\theta =\pi /2$ we have the classical values ${\mathrm{Re}}_{\mathrm{Orr}}=44.3$ for plane Couette flow and ${\mathrm{Re}}_{\mathrm{Orr}}=87.6$ for plane Poiseuille flow). Here the nondimensional interval between the planes bounding the channel is $[-1,1]$. In particular, these results improve those obtained by Joseph, who found for streamwise perturbations a critical nonlinear value of 20.65 in the plane Couette case, and those obtained by Joseph and Carmi who found the value 49.55 for plane Poiseuille flow for streamwise perturbations. If we fix some wavelengths from the experimental data and the numerical simulations, the critical Reynolds numbers that we obtain are in a very good agreement both with the the experiments and the numerical simulation. These results partially solve the Couette-Sommerfeld paradox.