Table of contents

We study transient work fluctuation relations (FRs) for Gaussian stochastic systems generating anomalous diffusion. For this purpose we use a Langevin approach by employing two different types of additive noise: (i) internal noise where the fluctuation–dissipation relation of the second kind (FDR II) holds, and (ii) external noise without FDR II. For internal noise we demonstrate that the existence of FDR II implies the existence of the fluctuation–dissipation relation of the first kind (FDR I), which in turn leads to conventional (normal) forms of transient work FRs. For systems driven by external noise we obtain violations of normal FRs, which we call anomalous FRs. We derive them in the long-time limit and demonstrate the existence of logarithmic factors in FRs for intermediate times. We also outline possible experimental verifications.

This paper aims to analyze the GPS traces of 258 volunteers in order to obtain a better understanding of both the human mobility patterns and the mechanism. We report the regular and scaling properties of human mobility for several aspects, and importantly we identify its Levy flight characteristic, which is consistent with those from previous studies. We further assume two factors that may govern the Levy flight property: (1) the scaling and hierarchical properties of the purpose clusters which serve as the underlying spatial structure, and (2) the individual preferential behaviors. To verify the assumptions, we implement an agent-based model with the two factors, and the simulated results do indeed capture the same Levy flight pattern as is observed. In order to enable the model to reproduce more mobility patterns, we add to the model a third factor: the jumping factor, which is the probability that one person may cancel their regular mobility schedule and explore a random place. With this factor, our model can cover a relatively wide range of human mobility patterns with scaling exponent values from 1.55 to 2.05.

We investigate the coarsening kinetics of an XY model defined on a square lattice when the underlying dynamics is governed by an energy-conserving Hamiltonian equation of motion. We find that the apparent superdiffusive growth of the length scale can be interpreted as the vortex mobility diverging logarithmically in the size of the vortex–antivortex pair, where the time dependence of the characteristic length scale can be fitted as L(t) ∼ ((t+t₀)ln(t+t₀))^1/2 with a finite offset time t₀. This interpretation is based on a simple phenomenological model of vortex–antivortex annihilation to explain the growth of the coarsening length scale L(t). The nonequilibrium spin autocorrelation function A(t) and the growing length scale L(t) are related by A(t) ≃ L^−λ(t) with a distinctive exponent of λ ≃ 2.21 (for E = 0.4) possibly reflecting the strong effect of propagating spin-wave modes. We also investigate the nonequilibrium relaxation (NER) of the system under sudden heating of the system from a perfectly ordered state to the regime of quasi-long-range order, which provides a very accurate estimation of the equilibrium correlation exponent η(E) for a given energy E. We find that both the equal-time spatial correlation C_nr(r,t) and the NER autocorrelation A_nr(t) exhibit scaling features consistent with the dynamic exponent of z_nr = 1.

The topological effects on the thermal properties of several knot configurations are investigated using Monte Carlo simulations. In order to check whether the topology of the knots is preserved during the thermal fluctuations we propose a method that allows very fast calculations and can be easily applied to arbitrarily complex knots. As an application, the specific energy and heat capacity of the trefoil, the figure-eight and the 8₁ knots are calculated at different temperatures and for different lengths. Short-range repulsive interactions between the monomers are assumed. The knot configurations are generated on a three-dimensional cubic lattice and sampled by means of the Wang–Landau algorithm and of the pivot method. The results obtained show that the topological effects play a key role for short-length polymers. Three temperature regimes of the growth rate of the internal energy of the system are distinguished.

We study the entanglement spectrum of Heisenberg spin ladders of arbitrary spin length S in the perturbative regime of strong rung coupling. For isotropic spin coupling the entanglement spectrum is, within first-order perturbation theory, always proportional to the energy spectrum of the single chain with a proportionality factor that is also independent of S. In particular, although the spin ladder possesses an excitation gap over its ground state for any spin length, the entanglement spectrum is gapless for half-integer S and gapful otherwise. A more complicated situation arises for anisotropic ladders of higher spin S ≥ 1 since here even the unperturbed ground state has a nontrivial entanglement spectrum. Finally we discuss related issues in dimerized spin chains.

A sign of topological order in a gapped one-dimensional quantum chain is the existence of edge zero modes. These occur in the Z₂-invariant Ising/Majorana chain, where they can be understood using free-fermion techniques. Here I discuss their presence in spin chains with Z_n symmetry, and prove that for appropriate couplings they are exact, even in this strongly interacting system. These modes are naturally expressed in terms of parafermions, generalizations of fermions to the Z_n case. I show that parafermionic edge zero modes do not occur in the usual ferromagnetic and antiferromagnetic cases, but rather only when the interactions are chiral, so that spatial-parity and time-reversal symmetries are broken.

We study analytically the distribution of fluctuations of the quantities whose average yields the usual two-point correlation and linear response functions in three unfrustrated models: the random walk, the d dimensional scalar field and the 2d XY model. In particular we consider the time dependence of ratios between composite operators formed with these fluctuating quantities which generalize the largely studied fluctuation-dissipation ratio, allowing us to discuss the relevance of the notion of effective temperature beyond linear order. The behavior of fluctuations in the aforementioned solvable cases is compared to numerical simulations of the 2d clock model with p = 6,12 states.

The mechanisms responsible for containing activity in systems represented by networks are crucial in various phenomena, for example, in diseases such as epilepsy that affect the neuronal networks and for information dissemination in social networks. The first models to account for contained activity included triggering and inhibition processes, but they cannot be applied to social networks where inhibition is clearly absent. A recent model showed that contained activity can be achieved with no need of inhibition processes provided that the network is subdivided into modules (communities). In this paper, we introduce a new concept inspired in the Hebbian theory, through which containment of activity is achieved by incorporating a dynamics based on a decaying activity in a random walk mechanism preferential to the node activity. Upon selecting the decay coefficient within a proper range, we observed sustained activity in all the networks tested, namely, random, Barabási–Albert and geographical networks. The generality of this finding was confirmed by showing that modularity is no longer needed if the dynamics based on the integrate-and-fire dynamics incorporated the decay factor. Taken together, these results provide a proof of principle that persistent, restrained network activation might occur in the absence of any particular topological structure. This may be the reason why neuronal activity does not spread out to the entire neuronal network, even when no special topological organization exists.

Most previous works study the evolution of cooperation in a structured population by commonly employing an isolated single network. However, realistic systems are composed of many interdependent networks coupled with each other, rather than an isolated single one. In this paper, we consider a system including two interacting networks with the same size, entangled with each other by the introduction of probabilistic interconnections. We introduce the public goods game into such a system, and study how the probabilistic interconnection influences the evolution of cooperation of the whole system and the coupling effect between two layers of interdependent networks. Simulation results show that there exists an intermediate region of interconnection probability leading to the maximum cooperation level in the whole system. Interestingly, we find that at the optimal interconnection probability the fraction of internal links between cooperators in two layers is maximal. Also, even if initially there are no cooperators in one layer of interdependent networks, cooperation can still be promoted by probabilistic interconnection, and the cooperation levels in both layers can more easily reach an agreement at the intermediate interconnection probability. Our results may be helpful in understanding cooperative behavior in some realistic interdependent networks and thus highlight the importance of probabilistic interconnection on the evolution of cooperation.

The mobility problem for suspensions of spherical particles immersed in an arbitrary flow of a viscous, incompressible fluid is considered in the regime of low Reynolds numbers. The scattering series which appears in the mobility problem is simplified. The simplification relies on the reduction of the number of types of single-particle scattering operators appearing in the scattering series. In our formulation there is only one type of single-particle scattering operator.

We previously introduced a time record model for use in studying the duration of sand–dust storms. In the model, X is the normalized wind speed and Xr is the normalized wind speed threshold for the sand–dust storm. X is represented by a random signal with a normal Gaussian distribution. The storms occur when X ≥ Xr. From this model, the time interval distribution of N = Aexp(−bt) can be deduced, wherein N is the number of time intervals with length greater than t, A and b are constants, and b is related to Xr.

In this study, sand–dust storm data recorded in spring at the Yanchi meteorological station in China were analysed to verify whether the time interval distribution of the sand–dust storms agrees with the above time interval distribution. We found that the distribution of the time interval between successive sand–dust storms in April agrees well with the above exponential equation. However, the interval distribution for the sand–dust storm data for the entire spring period displayed a better fit to the Weibull equation and depended on the variation of the sand–dust storm threshold wind speed.

The distribution function of the free energy fluctuations in one-dimensional directed polymers with free boundary conditions is derived by mapping the replicated problem to the N-particle quantum boson system with attractive interactions. It is shown that in the thermodynamic limit this function is described by the universal Tracy–Widom distribution of the Gaussian orthogonal ensemble.

In this paper, we provide a network growth model with incorporation into the ultimatum game dynamics. The network grows on the basis of the payoff-oriented preferential attachment mechanism, where a new node is added into the network and attached preferentially to nodes with higher payoffs. The interplay between the network growth and the game dynamics gives rise to quite interesting dynamical behaviors. Simulation results show the emergence of altruistic behaviors in the ultimatum game, which is affected by the growing network structure. Compared with the static counterpart case, the levels of altruistic behaviors are promoted. The corresponding strategy distributions and wealth distributions are also presented to further demonstrate the strategy evolutionary dynamics. Subsequently, we turn to the topological properties of the evolved network, by virtue of some statistics. The most studied characteristic path length and the clustering coefficient of the network are shown to indicate their small-world effect. Then the degree distributions are analyzed to clarify the interplay of structure and evolutionary dynamics. In particular, the difference between our growth network and the static counterpart is revealed. To explain clearly the evolved networks, the rich-club ordering and the assortative mixing coefficient are exploited to reveal the degree correlation.

The steady states of two gases of hard spheres or disks separated by an adiabatic piston in the presence of a temperature gradient are discussed. The temperature field is generated by two thermal walls at different temperatures, each of them in contact with one of the gases. The presence of the piston strongly affects the hydrodynamic fields, inducing a jump in its vicinity. A simple kinetic theory model is formulated. Its predictions are shown to be in good agreement with molecular dynamics simulation results. The applicability of the minimum entropy production principle is analyzed, and it is found that it only provides an accurate description of the system in the limit of a small temperature gradient.

Although every exactly known bond percolation critical threshold is the root in [0,1] of a lattice-dependent polynomial, it has recently been shown that the notion of a critical polynomial can be extended to any periodic lattice. The polynomial is computed on a finite subgraph, called the base, of an infinite lattice. For any problem with exactly known solution, the prediction of the bond threshold is always correct for any base containing an arbitrary number of unit cells. For unsolved problems, the polynomial is referred to as the generalized critical polynomial and provides an approximation that becomes more accurate with increasing number of bonds in the base, appearing to approach the exact answer. The polynomials are computed using the deletion–contraction algorithm, which quickly becomes intractable by hand for more than about 18 bonds. Here, I present generalized critical polynomials calculated with a computer program for bases of up to 36 bonds for all the unsolved Archimedean lattices, except the kagome lattice, which was considered in an earlier work. The polynomial estimates are generally within 10⁻⁵–10⁻⁷ of the numerical values, but the prediction for the (4,8²) lattice, though not exact, is not ruled out by simulations.

The ability to quantify the stochastic fluctuations present in biochemical and other systems is becoming increasing important. Analytical descriptions of these fluctuations are attractive, as stochastic simulations are computationally expensive. Building on previous work, a linear noise approximation is developed for biochemical models with many compartments, for example cells. The procedure is then implemented in the software package COPASI. This technique is illustrated with two simple examples and is then applied to a more realistic biochemical model. Expressions for the noise, given in the form of covariance matrices, are presented.

We investigate the dynamics of a single-ended N-state molecular zipper based on a model originally proposed by Kittel. The molecule is driven unidirectionally towards the completely unzipped state with increasing time t. The driving lowers the energies of states with k unzipped links by an amount proportional to kt. We solve the Pauli rate equation for the state probabilities and the partial differential equations, which yield the probability distributions for the work performed on the zipper and for the heat exchanged with the thermal reservoir. Similarly to the related equilibrium model, two different regimes can be identified at a given temperature with respect to the released molecular degrees of freedom per broken bond. In these two regimes the time evolution of the state probabilities as well as of the work and heat distributions shows a qualitatively different behavior.

We consider a family of estimation problems not admitting conventional analysis because of singularity and measurability issues. We define posterior distributions for the family by a variational technique analogous to that used to define Gibbs measures in statistical mechanics. The family of estimation problems, which arise in the asymptotic analysis of error-control codes, is parametrized by a code rate, R∈(0,∞); this is shown to be analogous to the absolute temperature of statistical mechanics. The family undergoes an (Ehrenfest) first-order phase transition at a critical code rate C (the channel capacity), where there is a convex set of posterior distributions. At all other code rates, there is only one posterior distribution; if R < C, this is the Dirac measure located at the source sequence, whereas if R > C it has infinite support. In a result reflecting the Dobrushin construction, we show that these posterior distributions are asymptotically consistent with those of families of finite-sequence error-control codes.

We study the effects of random scatterers on the ground state of the one-dimensional Lieb–Liniger model of interacting bosons on the unit interval in the Gross–Pitaevskii regime. We prove that Bose–Einstein condensation survives even a strong random potential with a high density of scatterers. The character of the wavefunction of the condensate, however, depends in an essential way on the interplay between randomness and the strength of the two-body interaction. For low density of scatterers and strong interactions the wavefunction extends over the whole interval. A high density of scatterers and weak interactions, on the other hand, lead to localization of the wavefunction in a fragmented subset of the interval.

Exact results on particle densities as well as correlators in two models of immobile particles, containing either a single species or else two distinct species, are derived. The models evolve following a descent dynamics through pair annihilation where each particle interacts once at most throughout its entire history. The resulting large number of stationary states leads to a non-vanishing configurational entropy. Our results are established for arbitrary initial conditions and are derived via a generating function method. The single-species model is the dual of the 1D zero-temperature kinetic Ising model with Kimball–Deker–Haake dynamics. In this way, both infinite and semi-infinite chains and also the Bethe lattice can be analysed. The relationship with the random sequential adsorption of dimers and weakly tapped granular materials is discussed.

The most general cyclic representations of the quantum integrable τ₂-model are analyzed. The complete characterization of the τ₂-spectrum (eigenvalues and eigenstates) is achieved in the framework of Sklyanin's separation of variables (SOV) method by extending and adapting previous results of one of the authors: (i) the determination of the τ₂-spectrum is reduced to the classification of the solutions of a given functional equation in a class of polynomials; (ii) the determination of the τ₂-eigenstates is reduced to the classification of the solutions of an associated Baxter equation. These last solutions are proved to be polynomials for a quite general class of τ₂-self-adjoint representations and the completeness of the associated Bethe ansatz type equations is derived. Finally, the following results are derived for the inhomogeneous chiral Potts model: (i) simplicity of the spectrum, for general representations; (ii) complete characterization of the chiral Potts spectrum (eigenvalues and eigenstates) and completeness of Bethe ansatz type equations, for the self-adjoint representations of the τ₂-model on the chiral Potts algebraic curves.

Rare event simulation and estimation for systems in equilibrium are among the most challenging topics in molecular dynamics. As was shown by Jarzynski and others, nonequilibrium forcing can theoretically be used to obtain equilibrium rare event statistics. The advantage seems to be that the external force can speed up the sampling of the rare events by biasing the equilibrium distribution towards a distribution under which the rare events are no longer rare. Yet algorithmic methods based on Jarzynski's and related results often fail to be efficient because they are based on sampling in path space. We present a new method that replaces the path sampling problem by minimization of a cross-entropy-like functional which boils down to finding the optimal nonequilibrium forcing. We show how to solve the related optimization problem in an efficient way by using an iterative strategy based on milestoning.

In this work we introduce a novel weighted message-passing algorithm based on the cavity method for estimating volume-related properties of random polytopes, properties which are relevant in various research fields ranging from metabolic networks, to neural networks, to compressed sensing. We propose, as opposed to adopting the usual approach consisting in approximating the real-valued cavity marginal distributions by a few parameters, using an algorithm to faithfully represent the entire marginal distribution. We explain various alternatives for implementing the algorithm and benchmarking the theoretical findings by showing concrete applications to random polytopes. The results obtained with our approach are found to be in very good agreement with the estimates produced by the Hit-and-Run algorithm, known to produce uniform sampling.

We investigate a balance network for the totally asymmetric simple exclusion process (TASEP). Subsystems consisting of TASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the TASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, it is well described using expressions in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems.

The model of directed compact percolation near a damp wall is generalized to allow for a bias in the growth of a cluster, either towards or away from the wall. The percolation probability for clusters beginning with seed width m, any distance from the wall, is derived exactly by solving the associated recurrences. It is found that the general biased case near a damp wall leads to a critical exponent β = 1, in line with the dry biased case, which differs from the unbiased damp/dry exponent β = 2.