In this paper, we are concerned with the crossover between strong disorder (SD) and weak disorder (WD) behaviors in three well-known problems that involve minimal paths: directed polymers (directed paths with fixed starting point and length), optimal paths (undirected paths with a fixed end-to-end or spanning distance), and undirected polymers (undirected paths with a fixed starting point and length). We present a unified theoretical framework from which we can easily deduce the scaling of the crossover point of each problem in an arbitrary dimension. Our theory is based on the fact that the SD limit behavior of these systems is closely related to the corresponding percolation problem. As a result, the properties of those minimal paths are completely controlled by the so-called red bonds of percolation theory. Our model is first addressed numerically and then approximated by a two-term approach. This approach provides us with an analytical expression that seems to be reasonably accurate. The results are in perfect agreement with our simulations and with most of the results reported in related works. Our research also leads us to propose this crossover point as a universal measure of the disorder strength in each case. Interestingly, that measure depends on both the statistical properties of the disorder and the topological properties of the network.

In the parameter spaces of nonlinear dynamical systems, we investigate the boundaries between periodicity and chaos and unveil the existence of fractal sets characterized by a singular fractal dimension that deviates greatly from the fractal sets in their vicinity. This extreme fractal dimension stands out from the typical value previously considered universal for these parameter boundaries. We show that such singular fractal sets dwell along parameter curves, called extreme curves, that intersect periodicity cascades at their centers of stability across all scales of parameter spaces. The results reported here are generally demonstrated for the class of one-dimensional maps with at least two control parameters. Generalizations to other classes of systems are possible.

We report higher-order coupling induced stable chimeralike state in a bipartite network of coupled phase oscillators without any time-delay in the coupling. We show that the higher-order interaction breaks the symmetry of the homogeneous synchronized state to facilitate the manifestation of symmetry breaking chimeralike state. In particular, such symmetry breaking manifests only when the pairwise interaction is attractive and higher-order interaction is repulsive, and vice versa. Further, we also demonstrate the increased degree of heterogeneity promotes homogeneous symmetric states in the phase diagram by suppressing the asymmetric chimeralike state. We deduce the low-dimensional evolution equations for the macroscopic order parameters using Ott-Antonsen ansatz and obtain the bifurcation curves from them using the software xppaut, which agrees very well with the simulation results. We also deduce the analytical stability conditions for the incoherent state, in-phase and out-of-phase synchronized states, which match with the bifurcation curves.

We present a detailed analysis of the dynamical behavior of an inhomogeneous Burridge-Knopoff model, a simplified mechanical model of an earthquake. Regardless of the size of seismic faults, a soil element rarely has a continuous appearance. Instead, their surfaces have complex structures. Thus, the model we suggest keeps the full Newtonian dynamics with inertial effects of the original model, while incorporating the inhomogeneities of seismic fault surfaces in stick-slip friction force that depends on the local structure of the contact surfaces as shown in recent experiments. The numerical results of the proposed model show that the cluster size and the moment distributions of earthquake events are in agreement with the Gutenberg-Richter law without introducing any relaxation mechanism. The exponent of the power-law size distribution we obtain falls within a realistic range of value without fine tuning any parameter. On the other hand, we show that the size distribution of both localized and delocalized events obeys a power law in contrast to the homogeneous case. Thus, no crossover behavior between small and large events occurs.

Cells sense environmental signals and transmit information intracellularly through changes in the abundance of molecular components. Such molecular abundances can be measured in single cells and exhibit significant heterogeneity in clonal populations even in identical environments. Experimentally observed joint probability distributions can then be used to quantify the covariability and mutual information between molecular abundances along signaling cascades. However, because stationary state abundances along stochastic biochemical reaction cascades are not conditionally independent, their mutual information is not constrained by the data-processing inequality. Here, we report the conditions under which the mutual information between stationary state abundances increases along a cascade of biochemical reactions. This nonmonotonic behavior can be intuitively understood in terms of noise propagation and time-averaging stochastic fluctuations that are short-lived compared to an extrinsic signal. Our results reemphasize that mutual information measurements of stationary state distributions of cellular components may be of limited utility for characterizing cellular signaling processes because they do not measure information transfer.

This paper considers similarities between statistical physics and Bayes inference through the Bayesian linear regression model. Some similarities have been discussed previously, such as the analogy between the marginal likelihood in Bayes inference and the partition function in statistical mechanics. In particular, this paper considers the proposal to associate discrete sample size with inverse temperature [C. H. LaMont and P. A. Wiggins, Phys. Rev. E 99, 052140 (2019)]. The previous study suggested that incorporating this similarity motivates the derivation of analogs of thermodynamic functions such as energy and entropy. The study also anticipated that those analogous functions have potential to describe Bayes estimation from physical points of view and to provide physical insights into mechanisms of estimation. This paper incorporates a macroscopic perspective as an asymptotics similar to the thermodynamic limit into the previous suggestion. Its motivation stems from the statistical mechanical concept of deriving thermodynamic functions that characterize macroscopic properties of macroscopic systems. This incorporation not only allows analogs of macroscopic thermodynamic functions to be considered but also suggests a candidate for an analog of inverse temperature with continuity, which is partly consistent with the previous proposal to associate the discrete sample size with inverse temperature. On the basis of this suggestion, we analyze analogs of macroscopic thermodynamic functions for a Bayesian linear regression model which is the basis of various machine learning models. We further investigate, through the behavior of these functions, how Bayes estimation is described from the perspective of physics and what kind of physical insight is obtained. As a result, the estimation of regression coefficients, which is the primary task of regression, appears to be described by the physical picture of balance between decreasing energy and increasing entropy as in equilibrium states of thermodynamic systems. More specifically we observe the physical view of Bayes inference as follows: the estimation succeeds where the effect of decreasing energy is dominant at low temperature. On the other hand, the estimation fails where the effect of increasing entropy is dominant at high temperature.

The general theoretical description of spin self-diffusion under a nonlinear gradient magnetic field is proposed, which extends the effective phase diffusion method for a linear gradient field. Based on the phase diffusion, the proposed method reveals the general features of phase evolutions in nonlinear gradient fields. There are three types of phase evolutions: phase diffusion, float phase evolution, and shift evolution based on the starting position. For spin diffusion near the origin of the nonlinear field, these three phase evolutions significantly affect the nuclear magnetic resonance (NMR) signal. The traditional methods have difficulties in handling these three-phase evolutions. Notably, the phase from float phase evolution is missed or misplaced in traditional methods, which leads to incorrect NMR signal attenuation or phase shift. The method here shows that the diffusing and float phase evolutions come from the first and second derivatives of the gradient field. Based on these three phase evolutions, the phase variance and corresponding NMR signal attenuation are obtained, as demonstrated by calculating the phase diffusions under both parabolic and cubic fields. The results indicate that signal attenuation obeys Gaussian attenuation for a short time, then changes to follow Lorentzian or Mittag-Leffler function attenuations as time increases, significantly different from Gaussian attenuation. For spins starting diffusion far away from the origin of the field gradient, the signal attenuation is Gaussian, but the float phase still has an important effect on the total phase shift of even-order gradient fields, which could be used to measure the diffusion coefficient directly. Random walk simulations were performed, which support the obtained theoretical results. General theoretical expressions are obtained, which can handle random order nonlinear gradient fields. The results could help develop advanced experimental techniques based on a nonlinear gradient field in NMR and magnetic resonance imaging.

We study the transport of rigid ellipsoidal swimmers in a periodic vortex array via numerical simulation and dynamical systems analysis. Via ensemble simulations, we show the counterintuitive result that slower swimming speeds can generate fast ballistic transport, while faster swimming speeds generate chaotic and diffusive transport, which is inherently slower in the long run. To explain this, we use the symmetry of the flow to construct a time-reversible Poincaré return map on a two-dimensional surface of section in phase space. For sufficiently small swimming speeds, we find stable periodic orbits on the surface of section surrounded by invariant tori, similar to Kolmogorov-Arnold-Moser curves. Trajectories within these tori are ballistic. As the swimming speed is increased, the periodic orbits undergo a sequence of period-doubling bifurcations that destroys the ballistic tori. These bifurcations exactly match the ballistic to diffusive transition from the ensemble simulations. Additional ensemble simulations are used to test the robustness of these results to noise. The ballistic behavior is destroyed as the strength of rotational diffusion increases. However, we estimate that the ballistic tori might still be seen in experiments.

Recent studies on reservoir computing essentially involve a high-dimensional dynamical system as the reservoir, which transforms and stores the input as a higher-dimensional state for temporal and nontemporal data processing. We demonstrate here a method to predict temporal and nontemporal tasks by constructing virtual nodes as constituting a reservoir in reservoir computing using a nonlinear map, namely, the logistic map, and a simple finite trigonometric series. We predict three nonlinear systems, namely, Lorenz, Rössler, and Hindmarsh-Rose, for temporal tasks and a seventh-order polynomial for nontemporal tasks with great accuracy. Also, the prediction is made in the presence of noise and found to closely agree with the target. Remarkably, the logistic map performs well and predicts close to the actual or target values. The low values of the root mean square error confirm the accuracy of this method in terms of efficiency. Our approach removes the necessity of continuous dynamical systems for constructing the reservoir in reservoir computing. Moreover, the accurate prediction for the three different nonlinear systems suggests that this method can be considered a general one and can be applied to predict many systems. Finally, we show that the method also accurately anticipates the time series of the all the three variable of Rössler system for the future (self-prediction).

Destructive agents, who opt out of the game and indiscriminately harm others, paradoxically foster cooperation, representing an intriguing variant of the voluntary participation strategy. Yet, their impact on cooperation remains inadequately understood, particularly in the context of pairwise social dilemma games and in comparison to their counterparts, constructive agents, who opt out of the game but indiscriminately benefit others. Furthermore, little is known about the combined effects of both agent types on cooperation dynamics. Using replicator dynamics in infinite and well-mixed populations, we find that contrary to their role in facilitating cooperation in multiplayer games, destructive agents fail to encourage cooperation in pairwise social dilemmas. Instead, they replace defection in the prisoners' dilemma and stag-hunt games. Similarly, in the chicken game, they can destabilize or replace the mixed equilibrium of cooperation and defection, undermining cooperation in the harmony (trivial) game. Conversely, constructive agents, when their payoffs exceed their contributions to opponents, can exhibit effects similar to destructive agents. However, if their payoffs are lower, while they destabilize defection in prisoners' dilemma and stag-hunt games, they do not disrupt the cooperation equilibrium in harmony games and have a negligible impact on the coexistence of cooperation in chicken games. The combination of destructive and constructive agents does not facilitate cooperation, but instead generates complex evolutionary dynamics, including bistable, tristable, and quadstable states, with outcomes contingent on their relative payoffs and game types. These results, taken together, enhance our understanding of the impact of the voluntary participation mechanism on cooperation, contributing to a more comprehensive understanding of its influence.

We numerically investigate the geometry and transport properties of infection fronts within the spatial SIR model in two dimensions. The model incorporates short-range correlated quenched random transmission rates. Our findings reveal that the critical average transmission rate for the steady-state propagation of the infection is overestimated by the naive mean-field homogenization. Furthermore, we observe that the velocity, profile, and harmfulness of the fronts, given a specific average transmission, are sensitive to the details of randomness. In particular, we find that the harmfulness of the front is larger the more uniform the transmission rate is, suggesting potential optimization in vaccination strategies under constraints like fixed average-transmission rates or limited vaccine resources. The large-scale geometry of the advancing fronts presents nevertheless robust universal features and, for a statistically isotropic and short-range correlated disorder, we get a roughness exponent $\alpha \approx 0.42\pm 0.10$ and a dynamical exponent $z\approx 1.6\pm 0.10$, which are roughly compatible with the one-dimensional Kardar-Parisi-Zhang (KPZ) universality class. We find that the KPZ term and the disorder-induced effective noise are present and have a kinematic origin.

The synthesis of ferroelectric nematic liquid crystals (FNLCs) concludes the long wait for their existence and potential usage in multiple liquid crystal based applications. In FNLCs, electric polarization in the nematic phase significantly decreases the switching time of in-on display pixels. In this article, we report the occurrence of translation symmetry breaking for heat propagation along the director field $\widehat{\mathit{n}}$ in the ferroelectric nematic phase. Due to the $C_{\infty V}$ symmetry of such a phase and close similarity to the bent-core polar liquid crystal phase, a rank-3 tensor describes its scalar order parameter and algebraic deductions. The finite element simulations show the occurrence of the nonsymmetrical thermal conductivity along $\widehat{\mathit{n}}$. The preferential heat transport in FNLCs can allow them to work as an all-thermal monophase non-nanostructured single-material thermal rectifier. We expect that this study will contribute towards the FNLCs application as functional layers and inks.

Fragmentation of a suspension of micron-sized plastic microparticles and their contraction into dense globules was experimentally obtained in a gas discharge plasma, when the plasma density was deliberately and abruptly increased. The globules took up spherical shapes 0.14–1.1 mm in diameters and contained from tens to thousands microparticles. The fragmentation and globule formation appears to be similar to the development of gravitational instability. This process is attributed to the Le Sage's like attraction among microparticles in a dense plasma due to the plasma losses inside a globule hypothesized theoretically in the middle of the 1990s. The key role of plasma flows in the attraction was prominently demonstrated in the same experiment by the distinctly visible disintegration of the globules when we reduced the density of the surrounding plasma to the initial one. Also molecular dynamics simulations of fragmentation of microparticle clouds and globules formation qualitatively resemble typical patterns of the fragmentation and collapse of interstellar nebulae.

We propose a statistical physics model of a neutral community, where each agent can represent identical plant species growing in the vertical direction with sunlight in the form of rich-get-richer competition. Disturbance added to this ecosystem, which makes an agent restart from the lowest growth level, is realized as a stochastic resetting. We show that in this model for sufficiently strong competition, vertical diversity characterized by a family of Hill numbers robustly emerges as a local maximum at intermediate disturbance.

To achieve fast computation, it is crucial to reset the memory to a desired state within a limited time. However, the inherent delay in the system's response often prevents reaching the desired state once the control process is completed in finite time. To address this challenge, we propose a shortcut strategy that incorporates an auxiliary control to guide the system towards an equilibrium state that corresponds to the intended control, thus enabling memory reset to desired accuracy regardless of the erasure speed. Through the application of thermodynamic geometry, we derive an optimal shortcut protocol for erasure processes that minimizes the energy cost. This research provides an effective design principle for realizing the finite-time erasure process to desired accuracy while simultaneously reducing the energy cost, thereby alleviating the burden of heat dissipation.

We study order-disorder transitions in three-dimensional multicolored loop models using Monte Carlo simulations. We show that the nature of the transition is intimately related to the nature of the loops. The symmetric loops undergo a first-order phase transition, while the nonsymmetric loops show a second-order transition. The critical exponents for the nonsymmetric loops are calculated. In three dimensions, the regular loop model with no interactions is dual to the $XY$ model. We argue that, due to interactions among the colors, the specific-heat exponent is found to be different from that of the regular loop model. The continuous nature of the transition is altered to a discontinuous one due to the strong intercolor interactions.

We conduct Monte Carlo simulations to analyze the percolation transition of a nonsymmetric loop model on a regular three-dimensional lattice. We calculate the critical exponents for the percolation transition of this model. The percolation transition occurs at a temperature that is close to, but not exactly, the thermal critical temperature. Our finite-size study on this model yields a correlation length exponent that agrees with that of the three-dimensional $XY$ model with an error margin of 6%.

Random network models, constrained to reproduce specific statistical features, are often used to represent and analyze network data and their mathematical descriptions. Chief among them, the configuration model constrains random networks by their degree distribution and is foundational to many areas of network science. However, configuration models and their variants are often selected based on intuition or mathematical and computational simplicity rather than on statistical evidence. To evaluate the quality of a network representation, we need to consider both the amount of information required to specify a random network model and the probability of recovering the original data when using the model as a generative process. To this end, we calculate the approximate size of network ensembles generated by the popular configuration model and its generalizations, including versions accounting for degree correlations and centrality layers. We then apply the minimum description length principle as a model selection criterion over the resulting nested family of configuration models. Using a dataset of over 100 networks from various domains, we find that the classic configuration model is generally preferred on networks with an average degree above 10, while a layered configuration model constrained by a centrality metric offers the most compact representation of the majority of sparse networks.

We study the problem of recovering a planted hierarchy of partitions in a network. The detectability of a single planted partition has previously been analyzed in detail and a phase transition has been identified below which the partition cannot be detected. Here we show that, in the hierarchical setting, there exist additional phases in which the presence of multiple consistent partitions can either help or hinder detection. Accordingly, the detectability limit for nonhierarchical partitions typically provides insufficient information about the detectability of the complete hierarchical structure, as we highlight with several constructive examples.