Although the high-fidelity state-to-state (StS) model accurately describes high-temperature thermochemical nonequilibrium flows, its practical application is hindered by the prohibitively high computational cost. In this paper, we develop a reduced-order model that leverages the widely used two-temperature (2T) framework and a coarse-grained treatment of molecular vibrational states to achieve accuracy comparable to the StS model while ensuring computational efficiency. We observe that the multigroup coarse-grained model (CGM), lumping vibrational energy levels into several groups, yields results close to the StS model for the high-temperature postshock oxygen flows, even using only two groups. However, the one-group CGM (CGM-1G), equivalent to the 2T model but using the StS kinetics, fails to approximate the StS results. Analysis of microscopic group properties reveals that the failure of the CGM-1G stems from the inability to capture the non-Boltzmann effects of mid-to-high vibrational levels, overestimating apparent dissociation rates and vibrational energy loss in the dissociation-dominated region. We then propose an analytical distribution function of vibrational groups by incorporating Treanor-like terms and an additional linear term (addressing the dissociation depletion of high-lying levels). Building upon this algebraic group distribution function and reconstructing vibrational levels within each group using the vibrational temperature, we develop a new 2T model called CG2T, which demonstrates accuracy much closer (than the CGM-1G) to the StS results for the postshock oxygen flows with varying degrees of thermochemical nonequilibrium. Moreover, a fullyconnected neural network is pretrained to substitute the module for the mass and vibrational energy source terms to enhance computational efficiency, achieving about 30-fold speedup in the CG2T model without sacrificing accuracy.

In this paper, we propose to solve the issues of long-range or next-neighbor interactions by introducing randomness. This approach is applied to the square lattice Ising model. The Monte Carlo method with the Metropolis algorithm is utilized to calculate the critical temperature $T_C^{*}$ under equilibrium thermodynamic phase transition conditions and to investigate the characterization of randomness in terms of magnetization. In order to further characterize the effect of this randomness on the magnetic system, clustering coefficients $C_p$ are introduced. Furthermore, we investigate a number of dynamic magnetic behaviors, including dynamic hysteresis behaviors and metamagnetic anomalies. The results indicate that noise has the effect of destabilizing the system and promoting the dynamic phase transition. When the system is subjected to noise, the effect of this noise can be mitigated by the addition of a time-oscillating magnetic field. Finally, the evolution of anomalous metamagnetic fluctuations under the influence of white noise is examined. The relationship between the bias field corresponding to the peak of the curve $h_{\mathrm{b}}^{\mathrm{peak}}$ and the noise parameter σ satisfies the exponential growth equation, which is consistent with other results.

The strategies for demixing and sorting mixed-chirality particles are crucial in the biochemical and pharmaceutical industries. However, whether chiral mixed particles can effectively separate in more complex spatial environments remains unresolved. In this paper, we explore the collective motion of binary chiral particle mixtures with environmental complex noise in the binary chiral Vicsek model (BCVM). We discover that the noisy region ratio, $\lambda$, significantly influences the separation behavior and spatial distribution of binary mixtures, unveiling system states not observed in uniform environments. Additionally, varying the chirality of particles reveals four distinct phases in our model. In the Vicsek bands phase (small chirality), an increase in $\lambda$ can, under certain conditions, promote segregation rather than consistently hindering the demixing process. Conversely, for large chirality, localized dynamics and a homogeneous phase emerge, reducing the impact of $\lambda$ on separation behavior. Notably, when chirality and activity are comparable, macrodrops and microflock phases appear, with a mixed-segregated state transition occurring at a critical ${\lambda }_c$. For $\lambda <{\lambda }_c$, chiral separation occurs with particles confined to the noise-free region. However, when $\lambda >{\lambda }_c$, particles gradually migrate to the noisy region, disrupting the separation. Further, we discuss the effects of multiple factors, including chirality, velocity, noise magnitude, particle number, and system size on ${\lambda }_c$. We also identify an optimal interaction radius at which ${\lambda }_c$ reaches its peak value. Our findings may inspire strategies for achieving spontaneous demixing and spatial migration of mixed-chirality particles in complex environments.

We study the thermodynamics of a crystalline solid by applying intermediate statistics obtained by deforming known solid state models using the mathematics of $q$ analogs. We apply the resulting $q$ deformation to both the Einstein and Debye models and study the deformed thermal and electrical conductivities and the deformed Debye specific heat. We find that the $q$ deformation acts in two different ways—but not necessarily as independent mechanisms. First, it acts as an effective factor of disorder or impurity, modifying the characteristics of a crystalline structure, which are phenomena described by $q$ bosons. Second, it also manifests intermediate statistics, namely, the $B$ anyons (or B-type systems). For the latter case we have identified the Schottky effect, normally associated with high-$T_c$ superconductors in the presence of rare-earth-ion impurities. We also find that it increases the specific heat of the solids beyond the Dulong-Petit limit at high temperature. Such an effect is usually related to anharmonicity of interatomic interactions. Alternatively, since in the $q$-boson's case the statistics are in principle maintained, the effect of the deformation acts more slowly due to a small change in the crystal lattice. On the other hand, $B$ anyons that belong to modified statistics are more sensitive to the deformation. The results reported here may be verified experimentally, for instance, in experimental samples by inserting impurities, or changes in pressure or temperature if one assumes these tuning quantities are related with the q-deformation parameter.

The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of $H(q,p)=K\left(p\right)+V\left(q\right)$ [with $K\left(p\right)$ replacing single $p^2$ contributions] is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing nonlinear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints.

To mitigate the pandemic stemming from COVID-19, numerous nations have initiated extensive vaccination campaigns for their citizens since late 2020. While affluent countries have predominantly received vaccine allocations, fewer doses have been dispatched to nations with lower average incomes. This unequal distribution not only widens the disparity between wealthy and impoverished regions but also prolongs the pandemic, evident in the emergence of new viral variants. Our research delves into the correlation between the duration of the pandemic and the timing of vaccine distribution between two countries with migratory ties. By using a pair of coupled susceptible-infected-recovered-deceased models incorporating vaccination data, we demonstrate that timely sharing of vaccines benefits both nations, regardless of the presence of viral variants. This underscores that in the realm of vaccine distribution, self-interest and altruism are not mutually exclusive.

Transcription is a stochastic process that involves several downstream operations which make it difficult to model and infer transcription kinetics from mature RNA numbers in individual cell. However, recent advances in single-cell technologies have enabled a more precise measurement of the fluctuations of nascent RNA that closely reflect transcription kinetics. In this paper we introduce a general stochastic model to mimic nascent RNA kinetics with complex promoter architecture. We derive the exact distribution and moments of nascent RNA using queuing theory techniques, which provide valuable insights into the effect of the molecular memory created by the multistep activation and deactivation on the stochastic kinetics of nascent RNA. Moreover, based on the analytical results, we develop a statistical method to infer the promoter memory from stationary nascent RNA distributions. Data analysis of synthetic data and a realistic example, the HIV-1 gene, verifies the validity of this inference method.

The flow of miscible electrolyte streams with mismatched electrical conductivities in the presence of a parallel applied electric field is known to exhibit electrokinetic instability (EKI). This paper deals with EKI in a configuration where the base state is established by electro-osmotic flow (EOF) of three coflowing streams, with the center stream having different conductivity than the sheath streams. All reported experiments of this EKI have shown that the instability exhibits either sinuous or varicose modes depending upon whether the center stream has higher or lower conductivity than the sheath streams, respectively. In this paper we elucidate the physical mechanism underlying the selection of these unstable modes in EKI using linear stability analysis. The stability analysis shows that the EOF simply convects the unstable modes besides establishing the base state. The instability occurs due to stationary convection cells, in the reference frame moving with the EOF, resulting from the coupling of the applied electric field with free charge in the regions with conductivity gradients. Importantly, we show that the unstable and stable disturbances for the configuration with a higher conductivity center stream have opposite stability characteristics when the center stream has lower conductivity than the sheath streams. Our analysis correctly explains the numerous experimental observations showing the consistent appearance of sinuous modes for higher conductivity and varicose modes for lower conductivity center streams.

We study statistical properties of matrix elements of observables written in the energy eigenbasis and truncated to small microcanonical windows. We present numerical evidence indicating that for all few-body operators in chaotic many-body systems, truncated below a certain energy scale, collective statistical properties of matrix elements exhibit emergent unitary symmetry. Namely, we show that below a certain scale the spectra of the truncated operators exhibit universal behavior, matching our analytic predictions, which are numerically testable for system sizes beyond exact diagonalization. We discuss operator and system-size dependence of the energy scale of emergent unitary symmetry and put our findings in the context of previous works exploring the emergence of random-matrix behavior at small energy scales.

We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)] showed the emergence of the $1/f^{\alpha }$ noise for the fitness observable with $\alpha \approx 1.2$ in one-dimension (1D) and $\alpha \approx 2$ for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, 4, and 5 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension ${\mathrm{D}}_u=4$, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into the return time statistics and the avalanche dimension.

Mixed spin-(1/2,1/2,1) trimer with two different Landé $g$ factors and two different exchange couplings is considered. The main feature of the model is nonconserving magnetization. The Hamiltonian of the system is diagonalized analytically. We presented a detailed analysis of the ground-state properties, revealing several possible ground-state phase diagrams and magnetization profiles. The main focus is on how nonconserving magnetization affects quantum entanglement. We have found that nonconserving magnetization can bring a continuous dependence of the entanglement quantifying parameter (negativity) on the magnetic field within the same eigenstate, while for the case of uniform $g$ factors it is a constant. The main result is an essential enhancement of the entanglement in the case of uniform couplings for one pair of spins caused by an arbitrary small difference in the values of $g$ factors. This enhancement is robust and brings almost a sevenfold increase of the negativity. We have also found a weakening of entanglement for other cases. Thus, nonconserving magnetization offers a broad opportunity to manipulate the entanglement by means of a magnetic field.

In the classical context, it is well known that, sometimes, if a search does not find its target, it is better to start the process anew. This is known as resetting. The quantum counterpart of resetting also indicates speeding up the detection process by eliminating the dark states, i.e., situations in which the particle avoids detection. In this work, we introduce the most probable position resetting (MPR) protocol, in which, at a given resetting step, resets are done with certain probabilities to the set of possible peak positions (where the probability of finding the particle is maximum) that could occur because of the previous resets and followed by uninterrupted unitary evolution, irrespective of which path was taken by the particle in previous steps. In a tight-binding lattice model, there exists a twofold degeneracy (left and right) of the positions of maximum probability. The survival probability with optimal restart rate approaches 0 (detection probability approaches 1) when the particle is reset with equal probability on both sides path independently. This protocol significantly reduces the optimal mean first-detected-passage time (FDT), and it performs better even if the detector is far apart compared to the usual resetting protocols in which the particle is brought back to the initial position. We propose a modified protocol, an adaptive two-stage MPR, by making the associated probabilities of going to the right and left a function of steps. In this protocol, we see a further reduction of the optimal mean FDT and improvement in the search process when the detector is far apart.

The sums of position- and momentum-space mutual information measures are used to examine the pairwise and higher-order statistical correlation in the ground states of $N$-particle coupled oscillators. Analytical expressions for these measures are shown to be related to the logarithmic interaction energies of these states, plus those of mirror states where the intensities of the one- and two-body potentials are interchanged, and the nature of the attractive or repulsive interaction is opposite to that in the original state. The measures separate the contributions from the interactions and those from the effective interactions due to marginalization into different terms. The pairwise mutual information sum is linearly related to the Shannon entropy sum in two particle systems, while the total correlation sum exhibits a similar relationship in three particle ones. In the latter instance, the interaction information sum can be related to entropy differences. This illustrates how entropy sums are connected to correlation measure sums in these systems. All measures approach zero with large $N$, when the magnitudes of the one- and two-body potentials are fixed. The pair mutual information and total correlation sums decay monotonically with $N$ in the presence of an attractive potential and monotonically increase with a repulsive potential. On the other hand, the interaction information sum exhibits a minimum at small $N$, with an attractive potential. This is a consequence of the higher-order correlations governing behavior at smaller $N$ while the pairwise ones dominate at larger $N$. Results are presented when the magnitude of the one-body potential is set to $N$.

The asymptotic scaling behavior of the Kuramoto model with finite populations has been notably elusive, despite comprehensive investigations employing both analytical and numerical methods. In this paper, we explore the Kuramoto model with “deterministic” sampling of natural frequencies, employing extensive numerical simulations and reporting the asymptotic values of the finite-size scaling exponents, which deviate significantly from the previously reported values in the literature. Additionally, we observe that these exponents are sensitive to the specifics of the sampling method. We discuss the origins of this variability through the self-consistent theory of entrained oscillators.

We consider an adaptive network of identical phase oscillators with the symmetric adaptation rule for the evolution of the connection weights under the influence of an external force. We show that the adaptive network exhibits a plethora of self-organizing dynamical states such as the two-cluster state, multiantipodal clusters, splay cluster, splay chimera, forced entrained state, chimera state, bump state, coherent, and incoherent states in the two-parameter phase diagrams. The intriguing structures of the frequency clusters and instantaneous phases of the oscillators characterize the distinct self-organized synchronized and partial synchronized states. The hierarchical organization of the frequency clusters, resulting in strongly coupled subnetworks, is also evident from the dynamics of the coupling weights, where the frequency clusters are either very weakly coupled or even completely decoupled from each other. Additionally, we also deduce the stability condition for the forced entrained state.

The structure of a complex network plays a crucial role in determining its dynamical properties. In this paper , we show that the the degree to which a network is directed and hierarchically organized is closely associated with the degree to which its dynamics break detailed balance and produce entropy. We consider a range of dynamical processes and show how different directed network features affect their entropy production rate. We begin with an analytical treatment of a two-node network followed by numerical simulations of synthetic networks using the preferential attachment and Erdös-Renyi algorithms. Next, we analyze a collection of 97 empirical networks to determine the effect of complex real-world topologies. Finally, we present a simple method for inferring broken detailed balance and directed network structure from multivariate time series and apply our method to identify non-equilibrium dynamics and hierarchical organisation in both human neuroimaging and financial time series. Overall, our results shed light on the consequences of directed network structure on non-equilibrium dynamics and highlight the importance and ubiquity of hierarchical organisation and non-equilibrium dynamics in real-world systems.

We have investigated, by Monte Carlo simulation, the orientational structure of very thin films of a discotic liquid crystal (DLC) confined between hybrid walls of controllable penetrability, as a function of wall separation $L_z$. Our purpose was to clarify whether, as predicted by continuum theory, the preferred orientation of the DLC is uniform, changes linearly, or changes discontinuously, when $L_z$ and the anchoring strengths at either wall are changed. The model consists of oblate hard Gaussian overlap (HGO) particles: each wall sees a particle as a disk of zero thickness and diameter $D$ less than or equal to that of the actual particle ${\sigma }_0$, embedded inside the particle and located halfway along, and perpendicular to, its minor axis. This provides a particle-level mechanism to control the anchoring properties of the walls, from planar (edge-on) for $D\sim 0$ to homeotropic (face-on) for $D\sim {\sigma }_0$, which can be done independently at either wall. As in our earlier work [C. Anquetil-Deck et al., J. Phys. Chem. B 124, 7709 (2020)], which was restricted to $L_z=6{\sigma }_0$, depending on the values of $D_s\equiv D/{\sigma }_0$ at the top ($D_s^t$) and bottom ($D_s^b$) walls, we find domains in $(D_s^b,D_s^t)$ space in which particle alignment is uniform planar (UP), uniform homeotropic (UH), or varies linearly from planar at one wall to homeotropic at the other (L), but no bistable or tristable regions are identified between these domains. Most importantly, there appears never to occur an abrupt change of the LC orientation when the walls strongly favor different anchorings, in general agreement with the scenario proposed by Velasco and co-workers [D. de las Heras et al., Phys. Rev. E 79, 011712 (2009)], but in contrast to the behavior of equivalent calamitic systems [F. Barmes et al., Phys. Rev. E 69, 061705 (2004); Phys. Rev. E, 71, 021705 (2005); C. Anquetil-Deck et al., Phys. Rev. E 86, 041707 (2012)]. However, for the thinnest films investigated ($L_z=2{\sigma }_0$), the system is unable to accommodate a rotation of the preferred particle orientation from one wall to the other and adopts instead a tilted configuration, similar to that reported earlier for Gay-Berne films in symmetric confinement [T. Gruhn et al., Thin Solid Films 330, 46 (1998); Mol. Phys. 93, 681 (1998)] but which, as far as we know, has been missed in most earlier work.

Kinetics of heterogeneous catalytic reactions are often complicated by various factors, and from the perspective of statistical physics the development of the corresponding models is frequently challenging especially in the case of practically important alloy catalysts. To extend the basics in this area, I use a generic kinetic model of ${\text{N}}_2$ formation in the NO reaction with such species as CO or ${\text{H}}_2$. The focus is on the reaction on the surface of a bimetallic alloy with low integral fraction of one of the metals so that the alloy is formed only at the surface. The main goal is to illustrate the specifics of the reaction kinetics and to clarify the accuracy of various approximations which are often inevitable for the analysis of such systems. The key results are as follows. (i) In the baseline one-metal case with the Langmuir-type equations, the model predicts the existence of the optimal adsorbate binding energy corresponding to the maximal reaction rate. (ii) With suitable substitution of the symbols, the equations employed for a uniform surface [item (i)] can be used for the mean-field description of reaction on the surface of a random alloy. In particular, the maximum in the dependence of the reaction rate on the binding energy is converted to the maximum with respect to the alloy composition. (iii) The reaction kinetics on the random-alloy surface have been described exactly. The corresponding maximum in the reaction rate is lower and somewhat smeared compared to that predicted in the mean-field approximation for an alloy or for the optimal monometallic catalyst. (iv) The reaction kinetics have been scrutinized also in the case of two-dimensional (2D) segregation of metal atoms at the surface in the limits of slow and rapid adsorbate diffusion between the spots. The kinetics are shown to be qualitatively different in these limits and also compared to the random-alloy case. (v) The thermodynamic criteria for 2D segregation of metal atoms at the surface have been derived as well.

Conventional measurements of two-phase flow in porous media often use completely immiscible fluids, or are performed over time scales of days to weeks. If applied to the study of gas storage and recovery, these measurements do not properly account for Ostwald ripening, significantly overestimating the amount of trapping and hysteresis. When there is transport of dissolved species in the aqueous phase, local capillary equilibrium is achieved: this may take weeks to months on the centimeter-sized samples on which measurements are performed. However, in most subsurface applications where the two phases reside for many years, equilibrium can be achieved. We demonstrate that in this case, two-phase displacement in porous media needs to be modeled as percolation without trapping. A pore network model is used to quantify how to convert measurements of trapped saturation, capillary pressure and relative permeability made ignoring Ostwald ripening to account for this effect. We show that conventional measurements overestimate the amount of capillary trapping by 20–25%.