We show that the Rényi entropy implies artificial biases not warranted by the data and incorrect updating information due to the finite size of the data despite being additive. It is demonstrated that this is so because it does not conform to the system and subset independence axioms of Shore and Johnson [J. IEEE Trans. Inf. Theory 26, 26 (1980)]. We finally show that the escort averaged constraints do not remedy the situation.

Tackling the critical transverse Ising ring with or without ring frustration, we establish the concept of nonlocality in a many-body system in the thermodynamic limit by calculating the nonlocal factors embedded in the factorizable correlation function. Through this exactly solvable prototype, we clearly show the intriguing difference between the periodic chains with odd and even numbers of lattice sites even in the thermodynamic limit. In the context of nonlocality, we also address the important application of finite-size scaling analysis by numerically working out the nonlocal factors of the isotropic $XY$ model and the spin-1/2 Heisenberg model.

We study the rectification of heat current in an $XXZ$ chain segmented in two parts. We model the effect of the environment with Lindblad heat baths. We show that in our system, rectification is large for strong interactions in half of the chain and if one bath is at a cold enough temperature. For the numerically accessible chain lengths, we observe that the rectification increases with the system size. We gain insight into the rectification mechanism by studying two-time correlations in the steady state. The presence of interactions also induces a strong nonlinear response to the temperature difference, resulting in superlinear and negative differential conductance regimes.

We explore here the feasibility of using the recently introduced Lagrangian descriptors [A. M. Mancho et al., Commun. Nonlinear Sci. Numer. Simul. 18, 3530 (2013)] to unveil the usually rich dynamics taking place in the vibrations of molecular systems, especially if they are floppy. The principal novelty of our work is the inclusion of $p$ norms in the definition of the descriptors in this kind of system, which greatly enhances their power to discern among the different structures existing in the phase space. As an illustration we use the LiCN molecule described by realistic potentials in two and three dimensions, which exhibits chaotic motion within a mixed phase space in the isomerization between the two wells corresponding to the linear isomer stable configurations, LiNC and LiCN. In particular, we pay special attention to the manifolds emerging from the unstable fixed point between the corresponding isomer wells, and also to the marginally stable structures around a parabolic point existing near the LiNC well.

The modeling of evolution in structured populations has been significantly advanced by evolutionary graph theory, which incorporates pairwise relationships between individuals on a network. More recently, a new framework has been developed to allow for multiplayer interactions of variable size in more flexible and potentially changing population structures. While the theory within this framework has been developed and simple structures considered, there has been no systematic consideration of a large range of different population structures, which is the subject of this paper. We consider a large range of underlying graphical structures for the territorial raider model, the most commonly used model in the new structure, and consider a variety of important properties of our structures with the aim of finding factors that determine the fixation probability of mutants. We find that the graphical temperature and the average group size, as previously defined, are strong predictors of fixation probability, while all other properties considered are poor predictors, although the clustering coefficient is a useful secondary predictor when combined with either temperature or group size. The relationship between temperature or average group size and fixation probability is sometimes, however, nonmonotonic, with a directional reverse occurring around the temperature associated with what we term “completely mixed” populations in the case of the hawk-dove game, but not the public goods game.

Many real-world complex systems are well represented as multilayer networks; predicting interactions in those systems is one of the most pressing problems in predictive network science. To address this challenge, we introduce two stochastic block models for multilayer and temporal networks; one of them uses nodes as its fundamental unit, whereas the other focuses on links. We also develop scalable algorithms for inferring the parameters of these models. Because our models describe all layers simultaneously, our approach takes full advantage of the information contained in the whole network when making predictions about any particular layer. We illustrate the potential of our approach by analyzing two empirical data sets: a temporal network of e-mail communications, and a network of drug interactions for treating different cancer types. We find that multilayer models consistently outperform their single-layer counterparts, but that the most predictive model depends on the data set under consideration; whereas the node-based model is more appropriate for predicting drug interactions, the link-based model is more appropriate for predicting e-mail communication.

Neurons process information by translating continuous signals into patterns of discrete spike times. An open question is how much information these spike times contain about signals which modulate either the mean or the variance of the somatic currents in neurons, as is observed experimentally. Here we calculate the exact information contained in discrete spike times about a continuous signal in both encoding strategies. We show that the information content about mean modulating signals is generally substantially larger than about variance modulating signals for biological parameters. Our analysis further reveals that higher information transmission is associated with a larger proportion of nonlinear signal encoding. Our study measures the complete information content of mean and variance coding and provides a method to determine what fraction of the total information is linearly decodable.

Direct numerical simulations of three-dimensional compressible helical turbulence are carried out at a grid resolution of ${1024}^3$ to investigate the effect of pressure, which is important for the joint cascade of kinetic energy and helicity in compressible helical turbulence. The principal finding is that the pressure term of the helicity equation [defined as ${\mathrm{\Phi }}^H=p{\partial }_i({\omega }_i/\rho )$] has a smaller effect on the helicity cascade in the aspect of amplitude and a smaller effective range, which leads to a longer inertial subrange of the helicity cascade, in contrast to a kinetic energy cascade. In addition, we also find that the effective range of ${\mathrm{\Phi }}^H$ is concentrated only in large scales statistically, which is similar to the effect of the pressure term of the kinetic energy equation (defined as ${\mathrm{\Phi }}^E=p{\partial }_i{u}_i$). From the overall sense of the effect of ${\mathrm{\Phi }}^E$ and ${\mathrm{\Phi }}^H$ on the kinetic energy and the helicity, respectively, both of them play a role of dissipation especially in the compression region. We propose that high enough helicity can affect the process of energy transformation between kinetic energy and internal energy, which means that the absolute local helicity hinders the process of kinetic energy transferring to internal energy, and promotes internal energy transferring to kinetic energy. In addition, ${\mathrm{\Phi }}^H$ plays a source role both for positive and negative helicity. We also study the mechanism of cancellations between compression and rarefaction regions, and we find that the impact of a shocklet on the helicity cascade can be ignored statistically.

Faraday waves are a classic example of a system in which an extended pattern emerges under spatially uniform forcing. Motivated by systems in which uniform excitation is not plausible, we study both experimentally and theoretically the effect of heterogeneous forcing on Faraday waves. Our experiments show that vibrations restricted to finite regions lead to the formation of localized subharmonic wave patterns and change the onset of the instability. The prototype model used for the theoretical calculations is the parametrically driven and damped nonlinear Schrödinger equation, which is known to describe well Faraday-instability regimes. For an energy injection with a Gaussian spatial profile, we show that the evolution of the envelope of the wave pattern can be reduced to a Weber-equation eigenvalue problem. Our theoretical results provide very good predictions of our experimental observations provided that the decay length scale of the Gaussian profile is much larger than the pattern wavelength.

We investigate a nonequilibrium phase transition in a dissipative and coherent quantum spin system using the quantum Langevin equation and mean-field theory. Recently, the quantum contact process (QCP) was theoretically investigated using the Rydberg antiblockade effect, in particular, when the Rydberg atoms were excited in $s$ states so that their interactions were regarded as being between the nearest neighbors. However, when the atoms are excited to $d$ states, the dipole-dipole interactions become effective, and long-range interactions must be considered. Here we consider a quantum spin model with a long-range QCP, where the branching and coagulation processes are allowed not only for the nearest-neighbor pairs but also for long-distance pairs, coherently and incoherently. Using the semiclassical approach, we show that the mean-field phase diagram of our long-range model is similar to that of the nearest-neighbor QCP, where the continuous (discontinuous) transition is found in the weak (strong) quantum regime. However, at the tricritical point, we find a new universality class, which was neither that of the QCP at the tricritical point nor that of the classical directed percolation model with long-range interactions. Implementation of the long-range QCP using interacting cold gases is discussed.

We study the dynamics of a one-dimensional run-and-tumble particle subjected to confining potentials of the type $V\left(x\right)={\alpha \left|x\right|}^p$, with $p>0$. The noise that drives the particle dynamics is telegraphic and alternates between $\pm 1$ values. We show that the stationary probability density $P\left(x\right)$ has a rich behavior in the $(p,\alpha )$ plane. For $p>1$, the distribution has a finite support in $[x_{-},x_{+}]$ and there is a critical line ${\alpha }_c\left(p\right)$ that separates an activelike phase for $\alpha >{\alpha }_c\left(p\right)$ where $P\left(x\right)$ diverges at $x_{\pm }$, from a passivelike phase for $\alpha <{\alpha }_c\left(p\right)$ where $P\left(x\right)$ vanishes at $x_{\pm }$. For $p<1$, the stationary density $P\left(x\right)$ collapses to a delta function at the origin, $P\left(x\right)=\delta \left(x\right)$. In the marginal case $p=1$, we show that, for $\alpha <{\alpha }_c$, the stationary density $P\left(x\right)$ is a symmetric exponential, while for $\alpha >{\alpha }_c$, it again is a delta function $P\left(x\right)=\delta \left(x\right)$. For the harmonic case $p=2$, we obtain exactly the full time-dependent distribution $P(x,t)$, which allows us to study how the system relaxes to its stationary state. In addition, for this $p=2$ case, we also study analytically the full distribution of the first-passage time to the origin. Numerical simulations are in complete agreement with our analytical predictions.

We consider a classic two-state switching diffusion model from a single-particle tracking perspective. The mean and the variance of the time-averaged mean square displacement (TAMSD) are computed exactly. When the measurement time (i.e., the trajectory duration) is comparable to or smaller than the mean residence times in each state, the ergodicity breaking parameter is shown to take arbitrarily large values, suggesting an apparent weak ergodicity breaking for this ergodic model. In this regime, individual random trajectories are not representative while the related TAMSD curves exhibit a broad spread, in agreement with experimental observations in living cells and complex fluids. Switching diffusions can thus present, in some cases, an ergodic alternative to commonly used and inherently non-ergodic continuous-time random walks that capture similar features.

The effects of uncorrelated white noise on a series of Josephson junctions coupled to a linear $RLC$ resonator are investigated. Both the cases of identical and nonidentical parameters are considered. The junctions are hysteretic, and hence can be considered birhythmic; that is, capable of oscillating at different frequencies for the same set of parameters. It is also found that, in the presence of noise, a uniform array behaves similarly to a single Josephson junction. However, the magnitude of the effective energy that characterizes the response to noise becomes smaller as the number of elements of the array increases, making the resonator less stable. Disorder in the parameters drastically changes the physics of the array. The disordered array of Josephson junctions misses the birhythmic properties for large values of the variance of the disorder parameter and remains birhythmic only for low values of the disorder parameter. Finally, disorder makes it difficult to locate the separatrix, hinting to a more complex structure of the effective energy landscape.

In the course of development, sleep, or mental disorders, certain neurons in the brain display spontaneous spike-burst activity. The synaptic plasticity evoked by such activity is here studied in the presence of spike-timing-dependent plasticity (STDP). In two chemically coupled bursting model neurons, the spike-burst activity can translate the STDP related to pre- and postsynaptic spike activity into burst-timing-dependent plasticity (BTDP), based on the timing of bursts of pre- and postsynaptic neurons. The resulting BTDP exhibits exponential decays with the same time scales as those of STDP. In weakly coupled bursting neuron networks, the synaptic modification driven by the spike-burst activity obeys a power-law distribution. The model can also produce a power-law distribution of synaptic weights. Here, the considered bursting behavior is made of stereotypical groups of spikes, and bursting is evenly spaced by long intervals.

Laser pulses traveling through a plasma can feature group velocities significantly differing from the speed of light in vacuum. This modifies the well-known Volkov states of an electron inside a strong laser-field from the vacuum case and, consequently, all quantum electrodynamical effects triggered by the electron. Here we present an in-depth study of the basic process of photon emission by an electron scattered from an intense short laser pulse inside a plasma, labeled nonlinear Compton scattering, based on modified Volkov solutions derived from first principles. Consequences of the nonlinear, plasma-dressed laser dispersion on the Compton spectra of emitted photons and implications for high-intensity laser-plasma experiments are pointed out. From a quantitative numerical evaluation we find the plasma to effectively suppress emission of low-frequency photons, whereas the emission of high-frequency photons is enhanced. The emission's angular distribution, on the other hand, is found to remain qualitatively unchanged with respect to the vacuum case.

Heat rectifiers are systems that conduct heat asymmetrically for forward and reversed temperature gradients. We present an analytical study of heat rectification in linear quantum systems. We demonstrate that asymmetric heat currents can be induced in a linear system only if it is dynamically driven. This asymmetry emerges when the driving frequency favors the nonsymmetric heat exchange processes at the expense of the symmetric ones. Finally, we demonstrate the feasibility of such driven harmonic network to work as a thermal transistor, quantifying its efficiency through the dynamical amplification factor.

We study the relaxation behavior of the Ornstein-Uhlenbeck (OU) process with time-dependent and fluctuating diffusivity. In this process, the dynamics of the position vector is modeled by the Langevin equation with a linear restoring force and a fluctuating diffusivity (FD). This process can be interpreted as a simple model of relaxational dynamics with internal degrees of freedom or in a heterogeneous environment. By utilizing the functional integral expression and the transfer matrix method, we show that the relaxation function can be expressed in terms of the eigenvalues and eigenfunctions of the transfer matrix for general FD processes. We apply our general theory to two simple FD processes where the FD is described by the Markovian two-state model or an OU-type process. We show analytic expressions of the relaxation functions in these models and their asymptotic forms. We also show that the relaxation behavior of the OU process with an FD is qualitatively different from those obtained from conventional models such as the generalized Langevin equation.

Work extraction from the Gibbs ensemble by a cyclic operation is impossible, as represented by the second law of thermodynamics. On the other hand, the eigenstate thermalization hypothesis (ETH) states that just a single energy eigenstate can describe a thermal equilibrium state. Here, we attempt to unify these two perspectives and investigate the second law at the level of individual energy eigenstates, by examining the possibility of extracting work from a single energy eigenstate. Specifically, we performed numerical exact diagonalization of a quench protocol of local Hamiltonians and evaluated the number of work-extractable energy eigenstates. We found that it becomes exactly zero in a finite system size, implying that a positive amount of work cannot be extracted from any energy eigenstate, if one or both of the prequench and the postquench Hamiltonians are nonintegrable. We argue that the mechanism behind this numerical observation is based on the ETH for a nonlocal observable. Our result implies that quantum chaos, characterized by nonintegrability, leads to a stronger version of the second law than the conventional formulation based on the statistical ensembles.