We derive integral quantum fluctuation theorems and quantum Jarzynski equalities for a feedback-controlled system and a memory which registers outcomes of the measurement. The obtained equalities involve the information content, which reflects the information exchange between the system and the memory, and take into account the back action of a general measurement contrary to the classical case. The generalized second law of thermodynamics under measurement and feedback control is reproduced from these equalities.

We demonstrate the existence of generalized synchronization in systems that act as mediators between two dynamical units that, in turn, show complete synchronization with each other. These are the so-called relay systems. Specifically, we analyze the Lyapunov spectrum of the full system to elucidate when complete and generalized synchronization appear. We show that once a critical coupling strength is achieved, complete synchronization emerges between the systems to be synchronized, and at the same point, generalized synchronization with the relay system also arises. Next, we use two nonlinear measures based on the distance between phase-space neighbors to quantify the generalized synchronization in discretized time series. Finally, we experimentally show the robustness of the phenomenon and of the theoretical tools here proposed to characterize it.

This paper introduces a spatiotemporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatiotemporal data. The model is derived as a spatial extension of a stochastic harmonic resonator model, which can be formulated in terms of a stochastic differential equation. The spatial structure is included by introducing linear operators, which affect both the oscillations and damping, and by choosing the appropriate spatial covariance structure of the driving time-white noise process. With the choice of the linear operators as partial differential operators, the resonator model becomes a stochastic partial differential equation, which is compatible with infinite-dimensional Kalman filtering. The resulting infinite-dimensional Kalman filtering problem allows for a computationally efficient solution as the computational cost scales linearly with measurements in the temporal dimension. This framework is applied to weather prediction and to physiological noise elimination in functional magnetic resonance imaging brain data.

The formation of a gel in a disperse coagulating system, wherein binary coagulation governs the temporal changes of the particle mass spectrum is studied for the coagulation kernel proportional to $K(g,l)=gl$ with $g,l$ being the numbers of monomers in the coalescing pair of particles. This model is known to reveal the sol-gel transition, i.e., the formation of one giant cluster with the mass comparable to the total mass of the whole system. This paper reports on some exact results that are valid for arbitrary initial particle mass spectra. The particle spectrum is shown to be expressed through a contour integral of the exponentiated initial generating function of the particle mass spectrum. The exact formula for the gel mass is derived for the scenario of passive gelation. Two scenarios of gelation, where the gel is either active or passive, are considered.

We present a small-angle x-ray scattering study of crystals formed by temperature-sensitive, swollen microgel particles consisting of poly($N$-isopropylacrylamide) copolymerized with acrylic acid and 5 mol % of a cross-linker. As for hard spheres, the random hexagonal close-packed structure is predominant during crystal growth and slowly transforms toward the face-centered-cubic structure. However, a transient phase of body-centered-cubic crystal is observed in an intermediate range of effective volume fractions. We estimate that the studied suspensions are close to a transition from face-centered-cubic to body-centered-cubic structure that can be understood by the tendency of the system to maximize the excluded volume and minimize the contact area between the particles.

Nonequilibrium molecular dynamics simulations of confined model liquids under pressure and sheared by the relative sliding of the boundary walls have been carried out. The relationship between the time-dependent traction coefficient, $\mu \left(t\right)$, and the state of internal structure of the film is followed from commencement of shear for various control parameters, such as applied load, global shear rate, and solid-liquid atom interaction parameters. Phase diagrams, velocity and temperature profiles, and traction coefficient diagrams are analyzed for pure Lennard-Jones (LJ) liquids and a binary LJ mixture. A single component LJ liquid is found to form semicrystalline arrangements with high-traction coefficients, and stick-slip behavior is observed for high pressures and low-shear velocities, which is shown to involve periodic deformation and stress release of the wall atoms and slip in the solid-liquid boundary region. A binary mixture, which discourages crystallization, gives a more classical tribological response with the larger atoms preferentially adsorbing commensurate with the wall. The results obtained are analyzed in the context of tribology: the binary mixture behaves like a typical lubricant, whereas the monatomic system behaves like a traction fluid. It is discussed how this type of simulation can give insights on the tribological behavior of realistic systems.

We consider the structure transitions in oblate supramicrometer nematic droplets related to reorientation of the line defect in the electric field. These transitions can be used in optical devices based on polymer dispersed liquid crystal materials with high contrast ratio. We suggest a simple method for determination of director distribution in nematic droplets of an arbitrary shape with surface interaction and in the presence of constant electric field. Point and linear defects are taken into account. This method does not require any presuppositions about symmetry of the director distribution. The elasticity continuum theory is treated with Monte Carlo annealing on a simple lattice. A special triangulation-based technique is applied for accurate representation of the droplet boundaries. The method is tested on 5CB material.

We demonstrate superionic ion conduction in simulations of a poly(ethylene oxide)-based polymer electrolyte. The superionic conduction uses cation hopping via chain-like ion aggregates, enabling long-range charge transfer while ions only move locally. The Na single-ion conductor achieves two essential features of superionic metal ion conductors: one-dimensional ion structure and immobile anions. The superionic conduction depends on the number and length of conduction pathways, the conduction pathway lifetime, and the rate at which end ions join and leave the pathway.

Nonlinear oscillators have been used to model neurons that fire periodically in the absence of input. These oscillators, which are called neuronal oscillators, share some common response structures with other biological oscillations such as cardiac cells. In this study, we analyze the dependence of the global dynamics of an impulse-driven stochastic neuronal oscillator on the relaxation rate to the limit cycle, the strength of the intrinsic noise, and the impulsive input parameters. To do this, we use a Markov operator that both reflects the density evolution of the oscillator and is an extension of the phase transition curve, which describes the phase shift due to a single isolated impulse. Previously, we derived the Markov operator for the finite relaxation rate that describes the dynamics of the entire phase plane. Here, we construct a Markov operator for the infinite relaxation rate that describes the stochastic dynamics restricted to the limit cycle. In both cases, the response of the stochastic neuronal oscillator to time-varying impulses is described by a product of Markov operators. Furthermore, we calculate the number of spikes between two consecutive impulses to relate the dynamics of the oscillator to the number of spikes per unit time and the interspike interval density. Specifically, we analyze the dynamics of the number of spikes per unit time based on the properties of the Markov operators. Each Markov operator can be decomposed into stationary and transient components based on the properties of the eigenvalues and eigenfunctions. This allows us to evaluate the difference in the number of spikes per unit time between the stationary and transient responses of the oscillator, which we show to be based on the dependence of the oscillator on past activity. Our analysis shows how the duration of the past neuronal activity depends on the relaxation rate, the noise strength, and the impulsive input parameters.

In this paper, we numerically investigate the robustness of cooperation clusters in prisoner's dilemma played on scale-free networks, where the network topologies change by continuous removal and addition of nodes. Each removal and addition can be either random or intentional. We therefore have four different strategies in changing network topology: random removal and random addition (RR), random removal and preferential addition (RP), targeted removal and random addition (TR), and targeted removal and preferential addition (TP). We find that cooperation clusters are most fragile against TR, while they are most robust against RP, even for large values of the temptation coefficient for defection. The effect of the degree mixing pattern of the network is not the primary factor for the robustness of cooperation under continuous change in network topology, which is quite different from the cases observed in static networks. Cooperation clusters become more robust as the number of links of hubs occupied by cooperators increase. Our results might infer the fact that a huge variety of individuals is needed for maintaining global cooperation in social networks in the real world where each node representing an individual is constantly removed and added.

We present a numerical study of dynamo action in a conducting fluid encased in a metallic spherical shell. Motions in the fluid are driven by differential rotation of the outer metallic shell, which we refer to as “the wall.” The two hemispheres of the wall are held in counter-rotation, producing a steady, axisymmetric interior flow consisting of differential rotation and a two-cell meridional circulation with radial inflow in the equatorial plane. From previous studies, this type of flow is known to maintain a stationary equatorial dipole by dynamo action if the magnetic Reynolds number is larger than about 300 and if the outer boundary is electrically insulating. We vary independently the thickness, electrical conductivity, and magnetic permeability of the wall to determine their effect on the dynamo action. The main results are the following: (a) Increasing the conductivity of the wall hinders the dynamo by allowing eddy currents within the wall, which are induced by the relative motion of the equatorial dipole field and the wall. This processes can be viewed as a skin effect or, equivalently, as the tearing apart of the dipole by the differential rotation of the wall, to which the field lines are anchored by high conductivity. (b) Increasing the magnetic permeability of the wall favors dynamo action by constraining the magnetic field lines in the fluid to be normal to the wall, thereby decoupling the fluid from any induction in the wall. (c) Decreasing the wall thickness limits the amplitude of the eddy currents, and is therefore favorable for dynamo action, provided that the wall is thinner than the skin depth. We explicitly demonstrate these effects of the wall properties on the dynamo field by deriving an effective boundary condition in the limit of vanishing wall thickness.

We consider kinematic dynamo action in rapidly rotating Boussinesq convection just above onset. The velocity is constrained to have either a square or a hexagonal pattern. For the square pattern, large-scale dynamo action is observed at onset, with most of the magnetic energy being contained in the horizontally averaged component. As the magnetic Reynolds number increases, small-scale dynamo action becomes possible, reducing the overall growth rate of the dynamo. For the hexagonal pattern, the breaking of symmetry between up and down flows results in an effective pumping velocity. For intermediate rotation rates, this additional effect can prevent the growth of any mean-field dynamo, so that only a small-scale dynamo is eventually possible at large enough magnetic Reynolds number. For very large rotation rates, this pumping term becomes negligible, and the dynamo properties of square and hexagonal patterns are qualitatively similar. These results hold for both perfectly conducting and infinite magnetic permeability boundary conditions.

We treat a turbulent velocity field as a message in the same way as a book or a picture. All messages can be described by their entropy per symbol $h$, defined as in Shannon's theory of communication. In a turbulent flow, as the Reynolds number Re increases, more correlated degrees of freedom are excited and participate in the turbulent cascade. Experiments in a turbulent soap film suggest that the spatial entropy density $h$ is a decreasing function of Re, namely $h\propto -\log \mathrm{Re}$ $+$ const. In the logistic map, also analyzed here, increasing the control parameter $r$ increases $h$. A modified logistic map with additional coupling to past iterations suggests the significance of correlations.

We introduce a class of networks that grow by enhanced redirection. Nodes are introduced sequentially, and each either attaches to a randomly chosen target node with probability $1-r$ or to the parent of the target with probability $r$, where $r$ is an increasing function of the degree of the parent. This mechanism leads to highly dispersed networks with unusual properties: (i) existence of multiple macrohubs—nodes whose degree is a finite fraction of the total number of network nodes $N$, (ii) lack of self-averaging, and (iii) anomalous scaling, in which $N_k$, the number of nodes of degree $k$ scales as $N_k\sim N^{\nu -1}/k^{\nu }$, with $1<\nu <2$.

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on $g$-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of $k$ integers to be $g$-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the $g$-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of $q$-Potts models in condensed matter physics are briefly discussed.

We investigate the interfacial instability of the steady uniform flow of a fluid-film layer down a permeable incline. A theoretical model is obtained by coupling the clear fluid flow equations governing the fluid film with Darcy's law for the filtration of fluid through the porous medium. A linear stability analysis is conducted and the effect of various parameters on the state of neutral stability is investigated. A simplified model is developed by reducing the dimensionality of the problem, which is then employed in order to determine the nonlinear effects on the stability of the equilibrium flow.

Complex network theory provides a powerful toolbox for studying the structure of statistical interrelationships between multiple time series in various scientific disciplines. In this work, we apply the recently proposed climate network approach for characterizing the evolving correlation structure of the Earth's climate system based on reanalysis data for surface air temperatures. We provide a detailed study of the temporal variability of several global climate network characteristics. Based on a simple conceptual view of red climate networks (i.e., networks with a comparably low number of edges), we give a thorough interpretation of our evolving climate network characteristics, which allows a functional discrimination between recently recognized different types of El Niño episodes. Our analysis provides deep insights into the Earth's climate system, particularly its global response to strong volcanic eruptions and large-scale impacts of different phases of the El Niño Southern Oscillation.

We have numerically studied heat conduction in a few one-dimensional momentum-conserving lattices with asymmetric interparticle interactions by the nonequilibrium heat bath method, the equilibrium Green-Kubo method, and the heat current power spectra analysis. Very strong finite-size effects are clearly observed. Such effects make the heat conduction obey a Fourier-like law in a wide range of lattice lengths. However, in yet longer lattice lengths, the heat conductivity regains its power-law divergence. Therefore, the power-law divergence of the heat conductivity in the thermodynamic limit is verified, as is expected by many existing theories.

We consider the Bethe equations for the isotropic spin-1/2 Heisenberg quantum spin chain with periodic boundary conditions. We formulate a conjecture for the number of solutions with pairwise distinct roots of these equations, in terms of numbers of so-called singular (or exceptional) solutions. Using homotopy continuation methods, we find all such solutions of the Bethe equations for chains of length up to 14. The numbers of these solutions are in perfect agreement with the conjecture. We also discuss an indirect method of finding solutions of the Bethe equations by solving the Baxter T-Q equation. We briefly comment on implications for thermodynamical computations based on the string hypothesis.

Focusing on isolated macroscopic systems, described in terms of either a quantum mechanical or a classical model, our two key questions are how far does an initial ensemble (usually far from equilibrium and largely unknown in detail) evolve towards a stationary long-time behavior (equilibration) and how far is this steady state in agreement with the microcanonical ensemble as predicted by statistical mechanics (thermalization). A recently developed quantum mechanical treatment of the problem is briefly summarized, putting particular emphasis on the realistic modeling of experimental measurements and nonequilibrium initial conditions. Within this framework, equilibration can be proven under very weak assumptions about those measurements and initial conditions, while thermalization still requires quite strong additional hypotheses. An analogous approach within the framework of classical mechanics is developed and compared with the quantum case. In particular, the assumptions to guarantee classical equilibration are now rather strong, while thermalization then follows under relatively weak additional conditions.