We investigate fluctuations of output work for a class of Stirling heat engines with working fluid composed of interacting units and compare these fluctuations to an average work output. In particular, we focus on engine performance close to a critical point where Carnot's efficiency may be attained at a finite power as reported by M. Campisi and R. Fazio [Nat. Commun. 7, 11895 (2016)]. We show that the variance of work output per cycle scales with the same critical exponent as the heat capacity of the working fluid. As a consequence, the relative work fluctuation diverges unless the output work obeys a rather strict scaling condition, which would be very hard to fulfill in practice. Even under this condition, the fluctuations of work and power do not vanish in the infinite system size limit. Large fluctuations of output work thus constitute inseparable and dominant element in performance of the macroscopic heat engines close to a critical point.

The Lévy walk process with rests is discussed. The jumping time is governed by an $\alpha$-stable distribution with $\alpha >1$ while a waiting time distribution is Poissonian and involves a position-dependent rate which reflects a nonhomogeneous trap distribution. The master equation is derived and solved in the asymptotic limit for a power-law form of the jumping rate. The relative density of resting and flying particles appears time-dependent, and the asymptotic form of both distributions obeys a stretched-exponential shape at large time. The diffusion properties are discussed, and it is demonstrated that, due to the heterogeneous trap structure, the enhanced diffusion, observed for the homogeneous case, may turn to a subdiffusion. The density distributions and mean squared displacements are also evaluated from Monte Carlo simulations of individual trajectories.

The balance equations for thermodynamic quantities are derived from the nonlocal quantum kinetic equation. The nonlocal collisions lead to molecular contributions to the observables and currents. The corresponding correlated parts of the observables are found to be given by the rate to form a molecule multiplied with its lifetime which can be considered as collision duration. Explicit expressions of these molecular contributions are given in terms of the scattering phase shifts. The two-particle form of the entropy is derived extending the Landau quasiparticle picture by two-particle molecular contributions. There is a continuous exchange of correlation and kinetic energies condensing into the rate of correlated variables for energy and momentum. For the entropy, an explicit gain remains and Boltzmann's H theorem is proved including the molecular parts of the entropy.

We analyze the statistics of gaps ($\mathrm{\Delta }H$) between successive avalanches in one-dimensional random-field Ising models (RFIMs) in an external field $H$ at zero temperature. In the first part of the paper we study the nearest-neighbor ferromagnetic RFIM. We map the sequence of avalanches in this system to a nonhomogeneous Poisson process with an $H$-dependent rate $\rho \left(H\right)$. We use this to analytically compute the distribution of gaps $P\left(\mathrm{\Delta }H\right)$ between avalanches as the field is increased monotonically from $-\infty$ to $+\infty$. We show that $P\left(\mathrm{\Delta }H\right)$ tends to a constant $\mathcal{C}\left(R\right)$ as $\mathrm{\Delta }H\to 0^{+}$, which displays a nontrivial behavior with the strength of disorder $R$. We verify our predictions with numerical simulations. In the second part of the paper, motivated by avalanche gap distributions in driven disordered amorphous solids, we study a long-range antiferromagnetic RFIM. This model displays a gapped behavior $P\left(\mathrm{\Delta }H\right)=0$ up to a system size dependent offset value $\mathrm{\Delta }{H}_{\text{off}}$, and $P\left(\mathrm{\Delta }H\right)\sim {(\mathrm{\Delta }H-\mathrm{\Delta }{H}_{\text{off}})}^{\theta }$ as $\mathrm{\Delta }H\to H_{\text{off}}^{+}$. We perform numerical simulations on this model and determine $\theta \approx 0.95\left(5\right)$. We also discuss mechanisms which would lead to a nonzero exponent $\theta$ for general spin models with quenched random fields.

This paper investigates the effects of bistability in a nonsmooth time-delayed dynamical system, which is often manifested in science and engineering. Previous studies on cutting dynamics have demonstrated persistent coexistence of chatter and chatter-free responses in a bistable region located in the linearly stable zone. As there is no widely accepted definition of basins of attraction for time-delayed systems, bistable regions are coined as unsafe zones (UZs). Hence, we have attempted to define the basins of attraction and stability basins for a typical delayed system to get insight into the bistability in systems with time delays. Special attention was paid to the influences of delayed initial conditions, starting points, and states at time zero on the long-term dynamics of time-delayed systems. By using this concept, it has been confirmed that the chatter is prone to occur when the waviness frequency in the workpiece surface coincides with the effective natural frequency of the cutting process. Further investigations unveil a thin “boundary layer” inside the UZ in the immediate vicinity of the stability boundary, in which we observe an extremely fast growth of the chatter basin stability. The results reveal that the system is more stable when the initial cutting depth is smaller. The physics of the tool deflection at the instant of the tool-workpiece engagement is used to evaluate the cutting safety, and the safe level could be zero when the geometry of tool engagement is unfavorable. Finally, the basins of attraction are used to quench the chatter by a single strike, where the resultant “islands” offer an opportunity to suppress the chatter even when the cutting is very close to the stability boundary.

The extent to which a temperature can be appropriately assigned to a small quantum system, as an internal property but not as a property of any large environment, is still an open problem. In this paper, a method is proposed for solving this problem, by which a studied small system is coupled to a two-level system as a probe, the latter of which can be measured by measurement devices. A main difficulty in the determination of possible temperature of the studied system comes from the back-action of the probe-system coupling to the system. For small quantum chaotic systems, we show that a temperature can be determined, the value of which is sensitive to neither the form, location, and strength of the probe-system coupling, nor the Hamiltonian and initial state of the probe. The temperature thus obtained turns out to have the form of Boltzmann temperature.

The importance of gap-junction coupling between $\beta$ cells in pancreatic islets is well established in mouse. Such ultrastructural connections synchronize cellular activity, confine biological heterogeneity, and enhance insulin pulsatility. Dysfunction of coupling has been associated with diabetes and altered $\beta$-cell function. However, the role of gap junctions between human $\beta$ cells is still largely unexplored. By using patch-clamp recordings of $\beta$ cells from human donors, we previously estimated electrical properties of these channels by mathematical modeling of pairs of human $\beta$ cells. In this work we revise our estimate by modeling triplet configurations and larger heterogeneous clusters. We find that a coupling conductance in the range $0.005–0.020$ nS/pF can reproduce experiments in almost all the simulated arrangements. We finally explore the consequence of gap-junction coupling of this magnitude between $\beta$ cells with mutant variants of the ATP-sensitive potassium channels involved in some metabolic disorders and diabetic conditions, translating studies performed on rodents to the human case. Our results are finally discussed from the perspective of therapeutic strategies. In summary, modeling of more realistic clusters with more than two $\beta$ cells slightly lowers our previous estimate of gap-junction conductance and gives rise to patterns that more closely resemble experimental traces.

Amorphous materials such as metallic, polymeric, and colloidal glasses exhibit complex preparation-dependent mechanical response to applied shear. In particular, glassy solids yield, with a mechanical response that transitions from elastic to plastic, with increasing shear strain. We perform numerical simulations to investigate the mechanical response of binary Lennard-Jones glasses undergoing athermal, quasistatic pure shear as a function of the cooling rate $R$ used to prepare them. The ensemble-averaged stress versus strain curve $\langle \sigma \left(\gamma \right)\rangle$ resembles the spatial average in the large size limit, which appears smooth and displays a putative elastic regime at small strains, a yielding-related peak in stress at intermediate strain, and a plastic flow regime at large strains. In contrast, for each glass configuration in the ensemble, the stress-strain curve $\sigma \left(\gamma \right)$ consists of many short nearly linear segments that are punctuated by particle-rearrangement-induced rapid stress drops. To explain the nonlinearity of $\langle \sigma \left(\gamma \right)\rangle$, we quantify the shape of the small stress-strain segments and the frequency and size of the stress drops in each glass configuration. We decompose the stress loss [i.e., the deviation in the slope of $\langle \sigma \left(\gamma \right)\rangle$ from that at $\langle \sigma \left(0\right)\rangle$] into the loss from particle rearrangements and the loss from softening [i.e., the reduction of the slopes of the linear segments in $\sigma \left(\gamma \right)$], and then compare the two contributions as a function of $R$ and $\gamma$. For the current studies, the rearrangement-induced stress loss is larger than the softening-induced stress loss, however, softening stress losses increase with decreasing cooling rate. We also characterize the structure of the potential energy landscape along the strain direction for glasses prepared with different $R$, and observe a dramatic change of the properties of the landscape near the yielding transition. We then show that the rearrangement-induced energy loss per strain can serve as an order parameter for the yielding transition, which sharpens for slow cooling rates and in large systems.

In this paper, we numerically study the dynamics of (1) a Newtonian liquid-filled capsule in a viscoelastic matrix and that of (2) a viscoelastic capsule in a Newtonian matrix in a linear shear flow using a front-tracking method. The numerical results for case (1) indicate that the polymeric fluid reduces the capsule deformation and aligns the deformed capsule with the flow direction. It also narrows the range of tension experienced by the deformed capsule for case (1), while the tank-treading period significantly increases. Interestingly, the polymeric fluid has an opposite effect on the tank-treading period and the orientation angle of case (2), but its effect on the deformation is similar to case (1).

The paper presents a method for simultaneous computation of eigenfunction and eigenvalue of the stationary Schrödinger equation on a grid, without imposing boundary-value condition. The method is based on the filter operator, which selects the eigenfunction from wave packet at the rate comparable to $\delta$ function. The efficacy and reliability of the method are demonstrated by comparing the simulation results with analytical or numerical solutions obtained by using other methods for various boundary-value conditions. It is found that the method is robust, accurate, and reliable. Further prospect of filter method for simulation of the Schrödinger equation in higher-dimensional space will also be highlighted.

We explore the formation and relaxation of the so-called quasistationary states (QSS) for particle distributions in three dimensions interacting via an attractive radial pair potential $V(r\to \infty )\sim 1/r^{\gamma }$ with $\gamma >0$, and either a soft core or hard core regularization at small $r$. In the first part of the paper, we generalize, for any spatial dimension $d\ge 2$, Chandrasekhar's approach for the case of gravity to obtain analytic estimates of the rate of collisional relaxation due to two-body collisions. The resultant relaxation rates indicate an essential qualitative difference depending on the integrability of the pair force at large distances: for $\gamma >d-1$, the rate diverges in the large particle number $N$ (mean-field) limit, unless a sufficiently large soft core is present; for $\gamma <d-1$, on the other hand, the rate vanishes in the same limit even in the absence of any regularization. In the second part of the paper we compare our analytical predictions with the results of extensive parallel numerical simulations in $d=3$ performed with an appropriate modification of the gadget code, for a range of different exponents $\gamma$ and soft cores leading to the formation of QSS. We find, just as for the previously well studied case of gravity (which we also revisit), excellent agreement between the parametric dependence of the observed relaxation times and our analytic predictions. Further, as in the case of gravity, we find that the results indicate that, when large impact factors dominate, the appropriate cutoff is the size of the system (rather than, for example, the mean interparticle distance). Our results provide strong evidence that the existence of QSS is robust only for long-range interactions with a large distance behavior $\gamma <d-1$; for $\gamma \ge d-1$, the existence of such states will be conditioned strongly on the short-range properties of the interaction.

The left-right chiral and ferromagnetic-antiferromagnetic double-spin-glass clock model, with the crucially even number of states $q=4$ and in three dimensions $d=3$, has been studied by renormalization-group theory. We find, for the first time to our knowledge, four spin-glass phases, including conventional, chiral, and quadrupolar spin-glass phases, and phase transitions between spin-glass phases. The chaoses, in the different spin-glass phases and in the phase transitions of the spin-glass phases with the other spin-glass phases, with the non-spin-glass ordered phases, and with the disordered phase, are determined and quantified by Lyapunov exponents. It is seen that the chiral spin-glass phase is the most chaotic spin-glass phase. The calculated phase diagram is also otherwise very rich, including regular and temperature-inverted devil's staircases and reentrances.

We address diffusion processes in a bounded domain, while focusing on somewhat unexplored affinities between the presence of absorbing and/or inaccessible boundaries. For the Brownian motion (Lévy-stable cases are briefly mentioned) model-independent features are established of the dynamical law that underlies the short-time behavior of these random paths, whose overall lifetime is predefined to be long. As a by-product, the limiting regime of a permanent trapping in a domain is obtained. We demonstrate that the adopted conditioning method, involving the so-called Bernstein transition function, works properly also in an unbounded domain, for stochastic processes with killing (Feynman-Kac kernels play the role of transition densities), provided the spectrum of the related semigroup operator is discrete. The method is shown to be useful in the case, when the spectrum of the generator goes down to zero and no isolated minimal (ground state) eigenvalue is in existence, like in the problem of the long-term survival on a half-line with a sink at origin.

By analyzing a paradigmatic example of the theory of dissipative systems—the classical and quantum dissipative standard map—we are able to explain the main features of the decay to the quantum equilibrium state. The classical isoperiodic stable structures typically present in the parameter space of these kinds of systems play a fundamental role. In fact, we have found that the period of stable structures that are near in this space determines the phase of the leading eigenstates of the corresponding quantum superoperator. Moreover, the eigenvectors show a strong localization on the corresponding periodic orbits (limit cycles). We show that this sort of scarring phenomenon (an established property of Hamiltonian and projectively open systems) is present in the dissipative case and it is of extreme simplicity.

We consider a globally coupled network of active (oscillatory) and inactive (nonoscillatory) oscillators with distributed-delay coupling. Conditions for aging transition, associated with suppression of oscillations, are derived for uniform and gamma delay distributions in terms of coupling parameters and the proportion of inactive oscillators. The results suggest that for the uniform distribution increasing the width of distribution for the same mean delay allows aging transition to happen for a smaller coupling strength and a smaller proportion of inactive elements. For gamma distribution with sufficiently large mean time delay, it may be possible to achieve aging transition for an arbitrary proportion of inactive oscillators, as long as the coupling strength lies in a certain range.

We compute universal distributions for the transition probabilities of a Markov model for transport in the mixed phase space of area-preserving maps and verify that the survival probability distribution for trajectories near an infinite island-around-island hierarchy exhibits, on average, a power-law decay with exponent $\gamma =1.57$. This exponent agrees with that found from simulations of the Hénon and Chirikov-Taylor maps. This provides evidence that the Meiss-Ott Markov tree model describes the transport for mixed systems.

We propose a stock market model which is investigated in the forms of difference and differential equations whose variables correspond to the demand or supply of each agent and to the price. In the model, agents are driven by the behavior of their trust contact network as well by fundamental analysis. By means of the deterministic version of the model, the connection between such drive mechanisms and the price is analyzed: imitation behavior promotes market instability, finitude of resources is associated to stock index stability, and high sensitivity to the fair price provokes price oscillations. Long-range correlations in the price temporal series and heavy-tailed distribution of returns are observed for the version of the model which considers different proposals for stochasticity of microeconomic and macroeconomic origins.

We analyze time evolution of statistical distributions of citations to scientific papers published in the same year. While these distributions seem to follow the power-law dependence we find that they are nonstationary and the exponent of the power-law fit decreases with time and does not come to saturation. We attribute the nonstationarity of citation distributions to different longevity of the low-cited and highly cited papers. By measuring citation trajectories of papers we found that citation careers of the low-cited papers come to saturation after 10–15 years while those of the highly cited papers continue to increase indefinitely: The papers that exceed some citation threshold become runaways. Thus, we show that although citation distribution can look as a power-law dependence, it is not scale free and there is a hidden dynamic scale associated with the onset of runaways. We compare our measurements to our recently developed model of citation dynamics based on copying-redirection-triadic closure and find explanations to our empirical observations.