Amorphous media at finite temperatures, be them liquids, colloids, or glasses, are made of interacting particles that move chaotically due to thermal energy, continuously colliding and scattering off each other. When the average configuration in these systems relaxes only at long times, one can introduce effective interactions that keep the mean positions in mechanical equilibrium. We introduce a framework to determine the effective force laws that define an effective Hessian that can be employed to discuss stability properties and the density of states of the amorphous system. We exemplify the approach with a thermal glass of hard spheres; these experience zero forces when not in contact and infinite forces when they touch. Close to jamming we recapture the effective interactions that at temperature $T$ depend on the gap $h$ between spheres as $T/h$ [C. Brito and M. Wyart, Europhys. Lett. 76, 149 (2006)]. For hard spheres at lower densities or for systems whose binary bare interactions are longer ranged (at any density), the emergent force laws include ternary, quaternary, and generally higher-order many-body terms, leading to a temperature-dependent effective Hessian.

We analytically study the role of nonconservative forces, namely viscous couplings, on the statistical properties of the energy flux between two Brownian particles kept at different temperatures. From the dynamical model describing the system, we identify an energy flow that satisfies a fluctuation theorem both in the stationary and in transient states. In particular, for the specific case of a linear nonconservative interaction, we derive an exact fluctuation theorem that holds for any measurement time in the transient regime, and which involves the energy flux alone. Moreover, in this regime the system presents an interesting asymmetry between the hot and cold particles. The theoretical predictions are in good agreement with the experimental results already presented in our previous article [Imparato et al., Phys. Rev. Lett. 116, 068301 (2016)], where we investigated the thermodynamic properties of two Brownian particles, trapped with optical tweezers, interacting through a dissipative hydrodynamic coupling.

We derive a concise and general expression of the energy dissipation rate for coupled oscillators rotating on circular trajectories by unifying the nonequilibrium aspects with the nonlinear dynamics via stochastic thermodynamics. In the framework of phase oscillator models, it is known that the even and odd parts of the coupling function express the effect on collective and relative dynamics, respectively. We reveal that the odd part always decreases the dissipation upon synchronization, while the even part yields a characteristic square-root change of the dissipation near the bifurcation point whose sign depends on the specific system parameters. We apply our theory to hydrodynamically coupled Stokes spheres rotating on circular trajectories that can be interpreted as a simple model of synchronization of coupled oscillators in a biophysical system. We show that the coupled Stokes spheres gain the ability to do more work on the surrounding fluid as the degree of phase synchronization increases.

To elucidate the nontrivial empirical statistical properties of fluctuations of a typical nonsteady time series representing the appearance of words in blogs, we investigated approximately $3\times {10}^9$ Japanese blog articles over a period of six years and analyze some corresponding mathematical models. First, we introduce a solvable nonsteady extension of the random diffusion model, which can be deduced by modeling the behavior of heterogeneous random bloggers. Next, we deduce theoretical expressions for both the temporal and ensemble fluctuation scalings of this model, and demonstrate that these expressions can reproduce all empirical scalings over eight orders of magnitude. Furthermore, we show that the model can reproduce other statistical properties of time series representing the appearance of words in blogs, such as functional forms of the probability density and correlations in the total number of blogs. As an application, we quantify the abnormality of special nationwide events by measuring the fluctuation scalings of 1771 basic adjectives.

Multilayer networks have been the subject of intense research during the past few years, as they represent better the interdependent nature of many real-world systems. Here, we address the question of describing the three different structural phases in which a multiplex network might exist. We show that each phase can be characterized by the presence of gaps in the spectrum of the supra-Laplacian of the multiplex network. We therefore unveil the existence of different topological scales in the system, whose relation characterizes each phase. Moreover, by capitalizing on the coarse-grained representation that is given in terms of quotient graphs, we explain the mechanisms that produce those gaps as well as their dynamical consequences.

Big Data has become the primary source of understanding the structure and dynamics of the society at large scale. The network of social interactions can be considered as a multiplex, where each layer corresponds to one communication channel and the aggregate of all of them constitutes the entire social network. However, usually one has information only about one of the channels or even a part of it, which should be considered as a subset or sample of the whole. Here we introduce a model based on a natural bilateral communication channel selection mechanism, which for one channel leads to consistent changes in the network properties. For example, while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one, we get a monotonically decreasing distribution as observed in empirical studies of single-channel data. We also find that assortativity may occur or get strengthened due to the sampling method. We analyze the far-reaching consequences of our findings.

Membrane-induced interactions can play a significant role in the spatial distribution of membrane-bound proteins. We develop a model that combines a continuum description of lipid bilayers with a discrete particle model of proteins to probe the emerging structure of the combined membrane-protein system. Our model takes into account the membrane's elastic behavior, the steric repulsion between proteins, and the quenching of membrane shape fluctuations due to the presence of the proteins. We employ coupled Langevin equations to describe the dynamics of the system. We show that coupling to the membrane induces an attractive interaction among proteins, which may contribute to the clustering of proteins in biological membranes. We investigate the lateral protein diffusion and find that it is reduced due to transient fluctuations in membrane shape.

We use a hybrid lattice Boltzmann method to study the behavior of sets of ferromagnetic colloidal disks in a nematic liquid crystal. When a weak rotating magnetic field acts on the system, the disks rotate following the magnetic field. This leads to a distortion in the liquid crystal that drives translational motion of the disks. If the concentration of disks is high, disks get locked together: a stable chain configuration is created, where each disk lays on the nearest neighbor. For intermediate concentrations of disks, a different behavior is observed. When disks are rotated by the magnetic field by more than ${90}^{\circ }$ from their initial orientation, the distortion in the liquid crystal leads to a simultaneous flip of both disks. The final disk positions depends only weakly on the initial configuration. Consecutive rotations of magnetic field push disks towards an equidistant configuration. Periodicity of the systems studied and analysis of the flipping motion of a single disk imply that one can use weak rotating magnetic fields to create stable crystal structures of disks.

A model, along with analytical and numerical solutions, is presented to describe a wide variety of one-dimensional slow flows of compressible heat-conductive fluids. The model is based on the approximation of uniform pressure valid for the flows, in which the sound propagation time is much shorter than the duration of any meaningful density variation in the system. The energy balance is described by the heat equation that is solved independently. This approach enables the explicit solution for the fluid velocity to be obtained. Interfacial and volumetric heat and mass sources as well as boundary motion are considered as possible sources of density variation in the fluid. A set of particular tasks is analyzed for different motion sources in planar, axial, and central symmetries in the quasistationary limit of heat conduction (i.e., for large Fourier number). The analytical solutions are in excellent agreement with corresponding numerical solutions of the whole system of the Navier-Stokes equations. This work deals with the ideal gas. The approach is also valid for other equations of state.

We identify and analyze the perfectly regular dripping mode of flow focusing. This mode occurs within narrow intervals of injected flow rates and applied pressure drops and leads to homogeneous-size droplets with diameters similar to or smaller than that of the discharge orifice. The balance between the local acceleration of the fluid particle and the applied pressure drop yields the scaling law for the droplet diameter. This scaling law is validated experimentally with excellent accord.

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) “Yukawa screening” and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

Structural transitions are examined in quasi-one-dimensional systems of freely rotating hard squares, which are confined between two parallel walls. We find two competing phases: one is a fluid where the squares have two sides parallel to the walls, while the second one is a solidlike structure with a zigzag arrangement of the squares. Using transfer matrix method we show that the configuration space consists of subspaces of fluidlike and solidlike phases, which are connected with low probability microstates of mixed structures. The existence of these connecting states makes the thermodynamic quantities continuous and precludes the possibility of a true phase transition. However, thermodynamic functions indicate strong tendency for the phase transition and our replica exchange Monte Carlo simulation study detects several important markers of the first order phase transition. The distinction of a phase transition from a structural change is practically impossible with simulations and experiments in such systems like the confined hard squares.

We report extensive numerical simulations of growth models belonging to the nonlinear molecular beam epitaxy (nMBE) class, on flat (fixed-size) and expanding substrates (ES). In both $d=1+1$ and $2+1$, we find that growth regime height distributions (HDs), and spatial and temporal covariances are universal, but are dependent on the initial conditions, while the critical exponents are the same for flat and ES systems. Thus, the nMBE class does split into subclasses, as does the Kardar-Parisi-Zhang (KPZ) class. Applying the “KPZ ansatz” to nMBE models, we estimate the cumulants of the $1+1$ HDs. Spatial covariance for the flat subclass is hallmarked by a minimum, which is not present in the ES one. Temporal correlations are shown to decay following well-known conjectures.

We introduce a class of discrete random-walk model driven by global memory effects. At any time, the right-left transitions depend on the whole previous history of the walker, being defined by an urnlike memory mechanism. The characteristic function is calculated in an exact way, which allows us to demonstrate that the ensemble of realizations is ballistic. Asymptotically, each realization is equivalent to that of a biased Markovian diffusion process with transition rates that strongly differs from one trajectory to another. Using this “inhomogeneous diffusion” feature, the ergodic properties of the dynamics are analytically studied through the time-averaged moments. Even in the long-time regime, they remain random objects. While their average over realizations recovers the corresponding ensemble averages, departure between time and ensemble averages is explicitly shown through their probability densities. For the density of the second time-averaged moment, an ergodic limit and the limit of infinite lag times do not commutate. All these effects are induced by the memory effects. A generalized Einstein fluctuation-dissipation relation is also obtained for the time-averaged moments.

We have studied zero-temperature metastable minima in classical $m$-vector component spin glasses in the presence of $m$-component random fields for two models, the Sherrington-Kirkpatrick (SK) model and the Viana-Bray (VB) model. For the SK model we have calculated analytically its complexity (the log of the number of minima) for both the annealed case where one averages the number of minima before taking the log and the quenched case where one averages the complexity itself, both for fields above and below the de Almeida-Thouless (AT) field, which is finite for $m>2$. We have done numerical quenches starting from a random initial state (infinite temperature state) by putting spins parallel to their local fields until there is no further decrease of the energy and found that in zero field it always produces minima that have zero overlap with each other. For the $m=2$ and $m=3$ cases in the SK model the final energy reached in the quench is very close to the energy $E_c$ at which the overlap of the states would acquire replica symmetry-breaking features. These minima have marginal stability and will have long-range correlations between them. In the SK limit we have analytically studied the density of states $\rho \left(\lambda \right)$ of the Hessian matrix in the annealed approximation. Despite the fact that in the presence of a random field there are no continuous symmetries, the spectrum extends down to zero with the usual $\sqrt{\lambda }$ form for the density of states for fields below the AT field. However, when the random field is larger than the AT field, there is a gap in the spectrum, which closes up as the AT field is approached. The VB model behaves differently and seems rather similar to studies of the three-dimensional Heisenberg spin glass in a random vector field.

The problem of a linear damped noisy oscillator is treated in the presence of two multiplicative sources of noise which imply a random mass and random damping. The additive noise and the noise in the damping are responsible for an influx of energy to the oscillator and its dissipation to the surrounding environment. A random mass implies that the surrounding molecules not only collide with the oscillator but may also adhere to it, thereby changing its mass. We present general formulas for the first two moments and address the question of mean and energetic stabilities. The phenomenon of stochastic resonance, i.e., the expansion due to the noise of a system response to an external periodic signal, is considered for separate and joint action of two sources of noise and their characteristics.

We investigate the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information. Specifically, we maximize the path entropy over discrete time step trajectories subject to normalization, stationarity, and detailed balance constraints together with a path-dependent dynamical information constraint reflecting a given average global behavior of the complex system. A general expression for the transition probability values associated with the stationary random Markov processes describing the nonequilibrium stationary system is computed. By virtue of our analysis, we uncover that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier of the general expression for the transition probability leads to a formal overlap with the well-known Glauber hyperbolic tangent rule for the transition probability for the stochastic Ising model in the limit of very high temperatures of the heat reservoir.

We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.

We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, $p$ variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.