We propose a family of ‘exactly solvable’ probability distributions to approximate partition functions of two-dimensional statistical mechanics models. While these distributions lie strictly outside the mean-field framework, their free energies can be computed in a time that scales linearly with the system size. This construction is based on a simple but nontrivial solution to the marginal problem

Run-and-tumble (RnT) motion is an example of active motility where particles move at constant speed and change direction at random times. In this work we study RnT motion with diffusion in a harmonic potential in one dimension via a path integral approach. We derive a Doi-Peliti field theory and use it to calculate the entropy production and other observables in closed form. All our results are exact

We derive generalized fluctuation–dissipation relations (FDR) holding for a general stochastic dynamics that includes as subcases both equilibrium models for passive colloids and non-equilibrium models used to describe active particles. The relations reported here differ from previous formulations of the FDR because of their simplicity: they require only the microscopic knowledge of the dynamics instead

We report numerical results aiming to unveil the role that the shape of asymmetric dumbbells has on the emergence of clogging in a two dimensional silo. To this end, dumbbells are designed adjoining two discs of different diameter giving rise to what are known as snowman shaped particles. Then, simulations performed for several outlet widths reveal that the standard case of a dumbbell conformed by

The loss surfaces of deep neural networks have been the subject of several studies, theoretical and experimental, over the last few years. One strand of work considers the complexity, in the sense of local optima, of high dimensional random functions with the aim of informing how local optimisation methods may perform in such complicated settings. Prior work of Choromanska etal (2015) established a

Neuronal ensemble inference is a significant problem in the study of biological neural networks. Various methods have been proposed for ensemble inference from experimental data of neuronal activity. Among them, Bayesian inference approach with generative model was proposed recently. However, this method requires large computational cost for appropriate inference. In this work, we give an improved

The social reinforcement mechanism, which characterizes the promoting effects when exposed to multiple sources in the social contagion process, is ubiquitous in information technology ecosystems and has aroused great attention in recent years. While the impacts of social reinforcement on single-layer networks are well documented, extension to multilayer networks is needed to study how reinforcement

In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process in networks. We analyze the global characteristics of the diffusive movement of random walkers on networks where the walkers hop considering the capacity of transport of each link. The links are susceptible to

We characterise the diffusion, mean-square speed, mean-square angular displacement, radial and speed probability distributions of toy robots called ‘hexbugs-nano’ that move on a dish antenna (with added surface roughness) simulating a harmonic well. It is observed that a model considering the system’s translational inertia but neglecting its moment of inertia, together with the inclusion of a constant

The inference performance of the pseudolikelihood method is discussed in the framework of the inverse Ising problem when the ℓ 2-regularized (ridge) linear regression is adopted. This setup is introduced for theoretically investigating the situation where the data generation model is different from the inference one, namely the model mismatch situation. In the teacher-student scenario under the assumption

We investigate the equilibration process of the strongly coupled quartic Fermi–Pasta–Ulam–Tsingou model by adding Langevin baths to the ends of the chain. The time evolution of the system is investigated by means of extensive numerical simulations and shown to match the results expected from equilibrium statistical mechanics in the time-asymptotic limit. Upon increasing the nonlinear coupling, the

Capillary imbibition of water plays a significant role in various applications at both the macroscopic and microscopic scales. However, it is still unclear whether capillary imbibition could be manipulated by the geometry structure of the nanotubes. In this paper, we adjust the concentric tube length difference ∆L of the double-walled nanotubes (DWNTs) to manipulate the capillary imbibition by molecular

This is the first in a series of papers devoted to generalisations of statistical loop models. We define a lattice model of webs on the honeycomb lattice, for n ⩾ 2. It is a statistical model of closed, cubic graphs with certain non-local Boltzmann weights that can be computed from spider relations. For n = 2, the model has no branchings and reduces to the well-known O(N) loop model introduced by Nienhuis

We introduce a mean-field framework for the study of systems of interacting particles sharing a conserved quantity. The work generalises and unites the existing fields of asset-exchange models, often applied to socio-economic systems, and aggregation-fragmentation models, typically used in modelling the dynamics of clusters. An initial model includes only two-body collisions, which is then extended

The formal derivatives of the Yang–Baxter equation with respect to its spectral parameters, evaluated at some fixed point of these parameters, provide us with two systems of differential equations. The derivatives of the R matrix elements, however, can be regarded as independent variables and eliminated from the systems, after which, two systems of polynomial equations are obtained in their place.

The Haldane phase is the prototype of symmetry protected topological (SPT) phases of spin chain systems. It can be protected by several symmetries having in common the degeneracy of the entanglement spectrum (ES). Here we explore in depth this degeneracy for the spin-1 Affleck–Kennedy–Lieb–Tasaki and bilinear-biquadratic Hamiltonians and show the emergence of a bulk-edge correspondence that relates

In this paper, we consider the grand partition function for an α-boson gas. First, we revisit the thermodynamic laws and functions in this formalism. Then, we explore α-boson gas condensation and show that the critical temperature at which α-boson condensation begins depends on the shape of the container. In particular, we compute the critical temperature for a cubic container. Finally, we discuss

The damage of the novel Coronavirus disease (COVID-19) is reaching an unprecedented scale. There are numerous classical epidemiology models trying to quantify epidemiology metrics. To forecast epidemics, classical approaches usually need parameter estimations, such as the contagion rate or the basic reproduction number. Here, we propose a data-driven, parameter-free, geometric approach to access the

The puzzling idea that the combination of independent estimates of the magnitude of a quantity results in a very accurate prediction, which is superior to any or, at least, to most of the individual estimates is known as the wisdom of crowds. Here we use the federal reserve bank of Philadelphia’s survey of professional forecasters database to confront the statistical and psychophysical explanations

The fracture stress of materials typically depends on the sample size and is traditionally explained in terms of extreme value statistics. A recent work reported results on the carrying capacity of long polyamide and polyester wires and interpret the results in terms of a probabilistic argument known as the St. Petersburg paradox. Here, we show that the same results can be better explained in terms

We investigate nonequilibrium steady states in a class of one-dimensional diffusive systems that can attain negative absolute temperatures. The cases of a paramagnetic spin system, a Hamiltonian rotator chain and a one-dimensional discrete linear Schrdinger equation are considered. Suitable models of reservoirs are implemented to impose given, possibly negative, temperatures at the chain ends. We show

The diffusion of particles with kappa distributed velocities is strongly influenced by statistical correlations. We argue that the consistent way to deduce the diffusion laws of any one degree of freedom is to analyze the simultaneous diffusion of virtually infinite correlated degrees of freedom. This is done by deriving the diffusion laws (I) by utilizing the superstatistics interpretation of the

We consider a one-dimensional run-and-tumble particle, or persistent random walk, in the presence of an absorbing boundary located at the origin. After each tumbling event, which occurs at a constant rate γ, the (new) velocity of the particle is drawn randomly from a distribution W(v). We study the survival probability S(x, t) of a particle starting from x ⩾ 0 up to time t and obtain an explicit expression

We present and analyze a minimalist model for the vertical transport of people in a tall building by elevators. We focus on start-of-day operation in which people arrive at the ground floor of the building at a fixed rate. When an elevator arrives on the ground floor, passengers enter until the elevator capacity is reached, and then they are transported to their destination floors. We determine the

We study how neural networks compress uninformative input space in models where data lie in d dimensions, but the labels of which only vary within a linear manifold of dimension d ∥ < d. We show that for a one-hidden-layer network initialized with infinitesimal weights (i.e. in the feature learning regime) trained with gradient descent, the first layer of weights evolves to become nearly insensitive

Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in this line of work is how to discretize the system in such a way that its stability and rates of convergence are preserved. In this paper we propose a geometric framework

We report experimental results of the speed–density relation emerging in pedestrian dynamics when individuals keep a prescribed safety distance among them. To this end, we characterize the movement of a group of people roaming inside an enclosure varying different experimental parameters: (i) global density, (ii) prescribed walking speed, and (iii) suggested safety distance. Then, by means of the Voronoi

Moving in the force-free potential and the tilted periodic potential, the diffusion of the under-damped particle subjected to correlated Lvy noise, i.e. the harmonic velocity Lvy noise, is investigated in this paper. We find that the underlying negative time correlation, especially the strong one, distinctly collides with the long-tailed nature of the noise, which results in a multi-diffusive process

Using the repulsive Blume–Emery–Griffiths model, we compute the phase diagram in three field spaces, temperature (T), crystal field (Δ), and magnetic field (H) on a complete graph in the canonical and microcanonical ensembles. For low biquadratic interaction strengths (K), a tricritical point exists in the phase diagram where three critical lines meet. As K decreases below a threshold value (which

In the present work, a power law dissipative Carnot-like heat engine cycle of two irreversible isothermal and two irreversible adiabatic processes with finite time non-adiabatic dissipation is considered and the efficiency under two optimization criteria figure of merit and efficient power, χ ep is studied. The generalized extreme bounds of the optimized efficiency under the above said optimization

Stochastic hybrid systems involve a coupling between a discrete Markov chain and a continuous stochastic process. If the latter evolves deterministically between jumps in the discrete state, then the system reduces to a piecewise deterministic Markov process. Well known examples include stochastic gene expression, voltage fluctuations in neurons, and motor-driven intracellular transport. In this paper

A general, multi-component Eulerian fluid theory is a set of nonlinear, hyperbolic partial differential equations. However, if the fluid is to be the large-scale description of a short-range many-body system, further constraints arise on the structure of these equations. Here we derive one such constraint, pertaining to the free energy fluxes. The free energy fluxes generate expectation values of currents

By working in the small persistence time limit, we determine the steady-state distribution of an active Ornstein Uhlenbeck particle (AOUP) experiencing, in addition to self-propulsion, a Gaussian white noise modeling a bath at temperature T. This allows us to derive analytical formulas for three quantities: the spatial density of a confined particle, the current induced by an asymmetric periodic potential

We study the statistical fluctuations of Lyapunov exponents in the discrete version of the non-integrable perturbed sine-Gordon equation, the dissipative AC- and DC-driven Frenkel–Kontorova model. Our analysis shows that the fluctuations of the exponent spacings in the strictly overdamped limit, which is nonchaotic, conform to an uncorrelated Poisson distribution. By studying the spatiotemporal dynamics

We investigate the tagged-particle motion in a strongly interacting quasi-confined liquid using periodic boundary conditions along the confining direction. Within a mode-coupling theory of the glass transition we calculate the self-nonergodicity parameters and the self-intermediate scattering function and compare them with event-driven molecular dynamics simulations. We observe non-monotonic behavior

We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time t max, exponentially distributed with mean inversely

We consider motion of an overdamped Brownian particle subject to stochastic resetting in one dimension. In contrast to the usual setting where the particle is instantaneously reset to a preferred location (say, the origin), here we consider a finite time resetting process facilitated by an external linear potential V(x) = λ|x|(λ > 0). When resetting occurs, the trap is switched on and the particle

In this paper, we study the local time spent by an Ornstein–Uhlenbeck (OU) particle at some location till time t. Using the Feynman–Kac formalism, the computation of the moment generating function (MGF) of the local time can be mapped to the problem of finding the eigenvalues and eigenfunctions of a quantum particle. We employ quantum perturbation theory to compute the eigenvalues and eigenfunctions

We present a comprehensive study about the relationship between the way detailed balance is broken in non-equilibrium systems and the resulting violations of the fluctuation–dissipation theorem. Starting from stochastic dynamics with both odd and even variables under time-reversal, we derive an explicit expression for the time-reversal operator, i.e. the Markovian operator which generates the time-reversed

Social gravity law widely exists in human travel, population migration, commodity trade, information communication, scientific collaboration and so on. Why is there such a simple law in many complex social systems is an interesting question. Although scientists from fields of statistical physics, complex systems, economics and transportation science have explained the social gravity law, a theoretical

A well-known characteristic of recent pandemics is the high level of heterogeneity in the infection spread: not all infected individuals spread the disease at the same rate and some individuals (superspreaders) are responsible for most of the infections. To quantify the effects of this phenomenon, we analyze the effect of the variance and higher moments of the infection distribution on the spread of

We propose a novel approach to the inverse Ising problem which employs the recently introduced density consistency approximation (DC) to determine the model parameters (couplings and external fields) maximizing the likelihood of given empirical data. This method allows for closed-form expressions of the inferred parameters as a function of the first and second empirical moments. Such expressions have

In this paper, the impact of crawling on evacuation dynamics is investigated via experiments and modeling. Two types of experiments are implemented, in which pedestrians are asked to escape out of a virtual room with an exit either by crawling or walking. The experiments show that escaping by crawling will increase the average evacuation time. Moreover, it is found that the evacuation time gap of crawling

We provide an economically sound micro-foundation to linear price impact models, by deriving them as the equilibrium of a suitable agent-based system. In particular, we retrieve the so-called propagator model as the high-frequency limit of a generalized Kyle model, in which the assumption of a terminal time at which fundamental information is revealed is dropped. This allows to describe a stationary

We consider the Y-systems satisfied by the , , vertex and loop models at roots of unity with twisted boundary conditions on the cylinder. The vertex models are the 6-, 15- and Izergin–Korepin 19-vertex models respectively. The corresponding loop models are the dense, fully packed and dilute Temperley–Lieb loop models respectively. For all three models, our focus is on roots of unity values of e iλ

Extracting a proper dynamic network for modeling a time-dependent complex system is an important issue. Building a correct model is related to finding out critical time points where a system exhibits considerable change. In this work, we propose to measure network similarity to detect proper time intervals. We develop three similarity metrics, node, link, and neighborhood similarities, for any consecutive

Which statistical features distinguish a meaningful text (possibly written in an unknown system) from a meaningless set of symbols? Here we answer this question by comparing features of the first half of a text to its second half. This comparison can uncover hidden effects, because the halves have the same values of many parameters (style, genre, etc). We found that the first half has more different

Binary random variables are the building blocks used to describe a large variety of systems, from magnetic spins to financial time series and neuron activity. In statistical physics the kinetic Ising model has been introduced to describe the dynamics of the magnetic moments of a spin lattice, while in time series analysis discrete autoregressive processes have been designed to capture the multivariate

The improvement of evacuation efficiency for pedestrians mixed with wheelchair users has practical significance to public safety. In this study, a series of pedestrian experiments are performed in corridors considering assisted wheelchair users. It is observed that an able-bodied pedestrian’s unimpeded speed and relaxation time are 38.9% higher and 24.5% shorter than those of wheelchair users, respectively

We determine the hydrodynamic modes of the superfluid analog of a smectic-A liquid crystal phase, i.e., a state in which both gauge invariance and translational invariance along a single direction are spontaneously broken. Such a superfluid smectic provides an idealized description of the incommensurate supersolid state realized in Bose–Einstein condensates with strong dipolar interactions as well

By the use of Monte Carlo simulation we study the critical behavior of a three-dimensional stochastic lattice model describing a diffusive epidemic propagation process. In this model, healthy (A) and sick (B) individuals diffuse on the lattice with diffusion constants d A and d B , respectively, and undergo reactions B → A and A + B → 2B. We determine the absorbing phase transition between a steady

The defining feature of active particles is that they constantly propel themselves by locally converting chemical energy into directed motion. This active self-propulsion prevents them from equilibrating with their thermal environment (e.g. an aqueous solution), thus keeping them permanently out of equilibrium. Nevertheless, the spatial dynamics of active particles might share certain equilibrium features

We explore the hypothesis that learning machines extract representations of maximal relevance, where the relevance is defined as the entropy of the energy distribution of the internal representation. We show that the mutual information between the internal representation of a learning machine and the features that it extracts from the data is bounded from below by the relevance. This motivates our

We propose three kinds of belief propagation (BP) guided decimation algorithms using asynchronous updating strategy to solve a prototype of random constraint satisfaction problem with growing domains referred to as model RB. For model RB, the exact satisfiability phase transitions have been established rigorously, and almost all instances are intrinsic hard in the transition region. Finding solutions

Fractional Brownian motion and the fractional Langevin equation are models of anomalous diffusion processes characterized by long-range power-law correlations in time. We employ large-scale computer simulations to study these models in two geometries, (i) the spreading of particles on a semi-infinite domain with an absorbing wall at one end and (ii) the stationary state on a finite interval with absorbing

The space of solutions of the exact renormalization group fixed point equations of the two-dimensional RP N−1 model, which we recently obtained within the scale invariant scattering framework, is explored for continuous values of N ⩾ 0. Quasi-long-range order occurs only for N = 2, and allows for several lines of fixed points meeting at the Berezinskii–Kosterlitz–Thouless transition point. A rich pattern

We propose a new way of measuring the correlation length in surface growth processes. We define a quantity in d = 1 + 1, where w(t) and L are the surface width of a given sample at time t and the system size, respectively, and ⟨…⟩ denotes the average over samples. The quantity R(L, t) is proportional to the correlation length and follows the relation R(L, t) ∼ t 1/z before the saturation for various

A conditioned stochastic process can display a very different behavior from the unconditioned process. In particular, a conditioned process can exhibit non-Gaussian fluctuations even if the unconditioned process is Gaussian. In this work, we revisit the Ferrari–Spohn model of a Brownian bridge conditioned to avoid a moving wall, which pushes the system into a large-deviation regime. We extend this

The Glosten–Milgrom model describes a single asset market, where informed traders interact with a market maker, in the presence of noise traders. We derive an analogy between this financial model and a Szilrd information engine by (i) showing that the optimal work extraction protocol in the latter coincides with the pricing strategy of the market maker in the former and (ii) defining a market analogue

We evaluate the significance of a recently proposed bivariate jump-diffusion model for a data-driven characterization of interactions between complex dynamical systems. For various coupled and non-coupled jump-diffusion processes, we find that the inevitably finite sampling interval of time-series data negatively affects the reconstruction accuracy of higher-order conditional moments that are required