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

For the 2D matrix Langevin dynamics that correspond to the continuous-time limit of the products of some 2 2 random matrices, the finite-time Lyapunov exponent can be written as an additive functional of the associated Riccati process submitted to some Langevin dynamics on the infinite periodic ring. Its large deviations properties can thus be analyzed from two points of view that are equivalent in

Along with experiments, numerical simulations are key to gaining insight into the underlying mechanisms governing domain wall motion in thin ferromagnetic systems. However, a direct comparison between numerical simulation of model systems and experimental results still represents a great challenge. Here, we present a tuned Ginzburg–Landau model to quantitatively study the dynamics of domain walls in

The two-dimensional easy-plane SU(3) magnet subjected to the transverse field was investigated with the exact-diagonalization method. So far, as to the XY model (namely, the easy-plane SU(2) magnet), the transverse-field-driven order–disorder phase boundary has been investigated with the exact-diagonalization method, and it was claimed that the end-point singularity (multicriticality) at the XX-symmetric

We consider quantum many body systems with generalized symmetries, such as the higher form symmetries introduced recently, and the ‘tensor symmetry’. We consider a general form of lattice Hamiltonians which allow a certain level of nonlocality. Based on the assumption of dual generalized symmetries, we explicitly construct low energy excited states. We also derive the ’t Hooft anomaly for the general

We derive the third-order poor man’s scaling equation for a generic Hamiltonian describing a quantum impurity embedded into an itinerant electron gas. We show that the XYZ Coqblin–Schrieffer model introduced by one of us earlier is algebraically renormalizable in the sense that the form of the Hamiltonian is preserved along the scaling trajectory, write down the scaling equations for the model, and

We model and calculate the fraction of infected population necessary to reach herd immunity, taking into account the heterogeneity in infectiousness and susceptibility, as well as the correlation between those two parameters. We show that these cause the effective reproduction number to decrease more rapidly, and consequently have a drastic effect on the estimate of the necessary percentage of the

The Landau equation is a kinetic equation based on the weak coupling approximation of the interaction between the particles. In the framework of dry active matter this new kinetic equation relies on the weak coupling approximation of both the alignment strength and the magnitude of the angular noise, instead of the hypothesis of diluteness. Therefore, it is a kinetic equation bridging between the Boltzmann

We consider a geometric modification of the asymmetric simple exclusion process model in which each site of a one-dimensional chain is attached to a lateral dead-end site. Since it has an uncorrelated steady state, this model shows rich density profile dynamics over large distances and timescales. We analyse various waves emerging from initial step-wise profiles. The most interesting feature is that

While a large number of studies have focused on the nonequilibrium dynamics of a system when it is quenched instantaneously from a disordered phase to an ordered phase, such dynamics have been relatively less explored when the quench occurs at a finite rate. Here, we study the slow quench dynamics in two paradigmatic models of classical statistical mechanics, a one-dimensional kinetic Ising model and

Gene expression (GE) is an inherently random or stochastic or noisy process. The randomness in different steps of GE, e.g., transcription, translation, degradation, etc., leading to cell-to-cell variations in mRNA and protein levels. This variation appears in organisms ranging from microbes to metazoans. Stochastic GE has important consequences for cellular function. The random fluctuations in protein

In infinite dimensions, many-body systems of pairwise interacting particles provide exact analytical benchmarks for the features of amorphous materials, such as the stress–strain curve of glasses under quasistatic shear. Here, instead of global shear, we consider an alternative driving protocol, as recently introduced by Morse etal 2020 (arXiv:2009.07706), which consists of randomly assigning a constant

We analyze the case of run-and-tumble particles pushed through a rugged channel both in the continuum and on the lattice. The current characteristic is non-monotone in the external field with the appearance of a current and nontrivial density profile even at zero field for asymmetric obstacles. If an external field is exerted against the direction of that zero-field current, then the resulting current

Site density functional theory (SDFT) provides a rigorous framework for statistical mechanics analysis of inhomogeneous molecular liquids. The key defining feature of these systems is the presence of two very distinct interactions scales (intra- and inter-molecular), and as such proper description of both effects is critical to the accuracy of the calculations. Current SDFT applications utilize the

It is known that the small-world structure constitutes sufficient conditions to sustain cooperation and thus enhances cooperation. On the contrary, the network with a very long average distance is usually thought of as suppressing the emergence of the cooperation. In this paper we show that the fractal structure, of which the average distance is very long, does not always play a negative role in the

Identifying the influential nodes to fragment a network is of significant importance in hindering the spread of epidemics and maximizing the influence of advertisements. Here, we address the problem by minimizing the largest eigenvalue of the non-backtracking matrices of networks, based on which a novel method is proposed to identify the optimal influential nodes. Interestingly, the proposed method

We perform numerical simulations of a long-range spherical spin glass with two and three body interaction terms. We study the gradient descent dynamics and the inherent structures found after a quench from initial conditions well thermalized at temperature T in. In very large systems, the dynamics perfectly agrees with the integration of the mean-field dynamical equations. In particular, we confirm

The synergy between experiment, theory, and simulations enables a microscopic analysis of spin-glass dynamics in a magnetic field in the vicinity of and below the spin-glass transition temperature T g. The spin-glass correlation length, ξ(t, t w; T), is analysed both in experiments and in simulations in terms of the waiting time t w after the spin glass has been cooled down to a stabilised measuring

While the canonical ensemble has been tremendously successful in capturing statistical properties of large systems, deviations from canonical behavior exhibited by small systems are not well understood. Here, using a two-dimensional small Ising magnet embedded inside a larger heat bath, we characterize the failures of the canonical ensemble when describing small systems. We find significant deviations

In a Markov chain population model subject to catastrophes, random immigration events (birth), promoting growth, are in balance with the effect of binomial catastrophes that cause recurrent mass removal (death). Using a generating function approach, we study two versions of such population models when the binomial catastrophic events are of a slightly different random nature. In both cases, we describe

The Braess paradox describes the counterintuitive situation that the addition of new roads to road networks can lead to higher travel times for all network users. Recently we could show that user optima leading to the paradox exist in networks of microscopic transport models. We derived phase diagrams for two kinds of route choice strategies that were externally tuned and applied by all network users

This work focuses on stochastic bifurcation for a slow–fast dynamical system driven by non-Gaussian α-stable Lvy noise. We prove the main result for the stochastic equilibrium states for the original system and the reduced system based on the random slow manifold. Then, it is verified that the slow reduced system bears the stochastic bifurcation phenomenon inherited from the original system. Furthermore

We present a numerical investigation of the density fluctuations in a model glass under cyclic shear deformation conditions. We demonstrate that in our model glass, the compressibility is suppressed in inherently minimally energetic structures, showing a hyperuniform trend at a density which is below the critical jamming density. At low shear amplitudes, i.e. below the yield amplitude, the system reaches

This paper is concerned with correlation functions of stochastic systems with memory, a prominent example being a molecule or colloid moving through a complex (e.g. viscoelastic) fluid environment. Analytical investigations of such systems based on non-Markovian stochastic equations are notoriously difficult. A common approximation is that of a single-exponential memory, corresponding to the introduction

We consider randomly flashing ratchets, where the potential acting can be switched to another at random time instants with Poisson statistics. Using coupled Fokker–Planck equations, we formulate explicit expressions of mean velocity, dispersion and quantities measuring thermodynamics. How potential landscapes and transitions affect the motility and energetics is exemplified by numerical calculations

Markov processes with stochastic resetting towards the origin generically converge towards non-equilibrium steady-states. Long dynamical trajectories can be thus analyzed via the large deviations at level 2.5 for the joint probability of the empirical density and the empirical flows, or via the large deviations of semi-Markov processes for the empirical density of excursions between consecutive resets

The macroscopic fluctuating theory developed during the last 30 years is applied to generic systems described by continuum fields ϕ(x, t) that evolve by a Langevin equation that locally either conserves or does not conserve the field. This paper aims to review well-known basic concepts and results from a pedagogical point of view by following a general framework in a practical and self-consistent way

Detecting the zero-temperature thermal order-by-disorder (ObD) transition in classical magnetic systems is notably difficult. We propose a method to probe this transition in an indirect way. The idea is to apply adequate and suitably engineered magnetic fields to transform the zero-temperature transition into a finite-temperature sharp crossover, which should be much easier to observe and characterise

Phase transition of the discrete Laplacian roughening model was investigated on a triangular lattice of various sizes by using the Wang–Landau (WL) Monte Carlo simulation and finite-size scaling analysis of partition-function zeros. The density of states was calculated using the WL method, and the internal energy and specific heat were calculated as a function of temperature. A single transition was

The universal scaling properties of the original and modified versions of the Villain–Lai–Das Sarma (VLDS) growth system are investigated numerically in both (1 + 1) and (2 + 1) dimensions. The modified VLDS equation with instability suppression by an exponentially decreasing function is equivalent to the VLDS with infinitely many weakly relevant nonlinear terms (VLDS∞). The growth instability and

The celebrated exchange fluctuation theorem—proposed by Jarzynski and Wjcik (2004 Phys. Rev. Lett. 92 230602) for heat exchange between two systems in thermal equilibrium at different temperatures—is explored here for quantum Gaussian states in thermal equilibrium. We employ the Wigner distribution function formalism for quantum states, which exhibits a close resemblance to the classical phase-space

Recently, we showed that optimization problems, both in infinite as well as in finite dimensions, for continuous variables and soft excluded volume constraints, can display entire isostatic phases where local minima of the cost function are marginally stable configurations endowed with non-linear excitations [1, 2]. In this work we describe an athermal adiabatic algorithm to explore with continuity

In this work, a geometrical representation of equilibrium and near equilibrium classical statistical mechanics is proposed. Within this formalism the equilibrium thermodynamic states are mapped on Euclidian vectors on a manifold of spherical symmetry. This manifold of equilibrium states can be considered as a Gauss map of the parametric representation of Gibbs classical statistical mechanics at equilibrium

Phase transitions do not necessarily correspond to a symmetry-breaking phenomenon. This is the case of the Kosterlitz–Thouless (KT) phase transition in a two-dimensional classical XY model, a typical example of a transition stemming from a deeper phenomenon than a symmetry-breaking. Actually, the KT transition is a paradigmatic example of the successful application of topological concepts to the study

Due to the broadband response characteristics at low levels of excitations, nonlinear multistable systems have garnered a great deal of attention in the area of energy harvesting. Moreover, various performance enhancement strategies of multistable harvesters have been proposed and discussed extensively for systems with perfectly symmetric potentials. However, it is very difficult or even impossible

In this paper, we introduce dyad social groups into the experiment to mimic uni- and bidirectional pedestrian flows that are closer to real life. According to the experimental videos, different strategies of collision avoidance for dyads are observed and classified. Moreover, we observe an interesting lane-merging phenomenon in bidirectional scenarios. Fundamental diagrams are calculated based on two

This study proposes a potential-based three-dimensional cellular automata model to describe the route choice behavior of pedestrians while evacuating terraced stands. The model takes into account the pedestrians’ states of sitting, standing, and moving, and the possible transitions on terraced stands. The proposed potential field algorithm reflects the influence on route choice behavior of heterogeneous

A fundamental problem in network science is the normalization of the topological or physical distance between vertices, which requires understanding the range of variation of the unnormalized distances. Here we investigate the limits of the variation of the physical distance in linear arrangements of the vertices of trees. In particular, we investigate various problems of the sum of edge lengths in

We investigate the connection between the supervised learning of the binary phase classification in the ferromagnetic Ising model and the standard finite-size-scaling theory of the second-order phase transition. Proposing a minimal one-free-parameter neural network model, we analytically formulate the supervised learning problem for the canonical ensemble being used as a training data set. We show

We identify a structure in the spectra of 1D lattice models of interacting electrons, characterised by an anomalous gapped branch of elementary excitations. Focussing on a family of Bethe ansatz solvable models, where all excitations are stable against decay, we make a four-way classification of the energy spectrum along with a model belonging to each class. We find in particular that the anomalous

Using systematic effective field theory, we explore the properties of antiferromagnetic films subjected to magnetic and staggered fields that are either mutually aligned or mutually orthogonal. We provide low-temperature series for the entropy density in either case up to two-loop order. Invoking staggered, uniform and sublattice magnetizations of the bipartite antiferromagnet, we investigate the subtle

The eight-vertex model on the square lattice with vertex weights a, b, c, d obeying the relation (a2 + ab)(b2 + ab) = (c2 + ab)(d2 + ab) is considered. Its transfer matrix with L = 2n + 1, n ⩾ 0, vertical lines and periodic boundary conditions along the horizontal direction has the doubly-degenerate eigenvalue Θn = (a + b)2n+1. A basis of the corresponding eigenspace is investigated. Several scalar

Heterogeneity and difference in the dynamics of individual reputation may strongly affect learning behavior, and hence also the evolution of cooperation within a population. Motivated by this, we propose here an evolutionary spatial multigames model, wherein the reputation of an individual increases if they cooperate and decreases if they defect. After the payoffs are determined, individuals with a

Link prediction is a challenging research topic that comes along with the prevalence of network data analysis. Compared with traditional link prediction, determining future links in temporal directed networks is more complicated. In this paper, we introduce a novel link prediction method based on non-negative tensor factorization that takes into account the link direction and temporal information.

Stochastic differential equations are widely used in various fields; in particular, the usefulness of duality relations has been demonstrated in some models such as population models and Brownian momentum processes. In this study, a discussion based on combinatorics is made and applied to calculate the expectation values of functions in systems in which evolution is governed by stochastic differential

Communication networks, power grids, and transportation networks are all examples of networks whose performance depends on reliable connectivity of their underlying network components even in the presence of usual network dynamics due to mobility, node or edge failures, and varying traffic loads. Percolation theory quantifies the threshold value of a local control parameter such as a node occupation

In this paper, we study matrix-product unitary operators (MPUs) for fermionic one-dimensional chains. In stark contrast to the case of 1D qudit systems, we show that (i) fermionic MPUs (fMPUs) do not necessarily feature a strict causal cone and (ii) not all fermionic quantum cellular automata (QCA) can be represented as fMPUs. We then introduce a natural generalization of the latter, obtained by allowing

The open XXZ spin chain with the anisotropy parameter and diagonal boundary magnetic fields that depend on a parameter x is studied. For real x > 0, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly computed. In a suitable normalisation, the ground-state components are characterised as polynomials in x with integer coefficients. Linear sum rules and special components

We investigate theoretically the effects of periodic-in-time modulations on the properties of earthquakes. To wit, we consider successively the one dimensional Burridge–Knopoff (BK) model and the two dimensional Olami–Feder–Christensen (OFC) model. Each model is modified to take into account either a modulation of normal stress or of shear stress acting on a fault. Despite the differences between the

All statistical information about heat can be obtained with the probability distribution of the heat functional. This paper derives analytically the expression for the distribution of the heat, through path integral, for a diffusive system in a logarithm potential. We apply the found distribution to the first passage problem and find unexpected results for the reversibility of the distribution, giving

In this work, from the perspective of statistical mechanics, the statistical properties of charged-particle motion in a microwave field and a magnetic field with a general direction described by a generalized Langevin equation subjected to an intrinsic noise with a power-law time decay correlation function have been studied. Using the general expansion theorem for the Laplace transform, the drift velocity

The combined action of noise and deterministic force in dynamical systems can induce resonant effects. Here, we demonstrate a minimal, deterministic force-free setup allowing for the occurrence of resonant, noise-induced effects. We show that in the archetypal problem of escape from finite intervals driven by α-stale noise with a periodically modulated stability index, depending on the initial direction

We establish some limit theorems for the elephant random walk (ERW), including Berry–Esseen’s bounds, Cramr moderate deviations and local limit theorems. These limit theorems can be regarded as refinements of the central limit theorem for the ERW. Moreover, by these limit theorems, we conclude that the convergence rate of normal approximations and the domain of attraction of normal distribution mainly