Multilevel autonomous quantum thermal machines are discussed. In particular, we explore the relationship between the size of the machine (captured by Hilbert space dimension) and the performance of the machine. Using the concepts of virtual qubits and virtual temperatures, we show that higher dimensional machines can outperform smaller ones. For instance, by considering refrigerators with more levels, lower temperatures can be achieved, as well as higher power. We discuss the optimal design for refrigerators of a given dimension. As a consequence we obtain a statement of the third law in terms of Hilbert space dimension: Reaching absolute zero temperature requires infinite dimension. These results demonstrate that Hilbert space dimension should be considered a thermodynamic resource.

We study the dynamics and acoustics of a nonlinear lattice with fixed boundary conditions composed of a finite number of particles coupled by linear springs, undergoing in-plane oscillations. The source of the strongly nonlinearity of this lattice is geometric effects generated by the in-plane stretching of the coupling linear springs. It has been shown that in the limit of low energy the lattice gives rise to a strongly nonlinear acoustic vacuum, which is a medium with zero speed of sound as defined in classical acoustics. The acoustic vacuum possesses strongly nonlocal coupling effects and an orthogonal set of nonlinear standing waves [or nonlinear normal modes (NNMs)] with mode shapes identical to those of the corresponding linear lattice; in contrast to the linear case, however, all NNMs except the one with the highest wavelength are unstable. In addition, the lattice supports two types of waves, namely, nearly linear sound waves (termed “$L$ waves”) corresponding to predominantly axial oscillations of the particles and strongly nonlinear localized propagating pulses (termed “$NL$ pulses”) corresponding to predominantly transverse oscillating wave packets of the particles with localized envelopes. We show the existence of nonlinear nonreciprocity phenomena in the dynamics and acoustics of the lattice. Two opposite cases are examined in the limit of low energy. The first gives rise to nonreciprocal dynamics and corresponds to collective, spatially extended transverse loading of the lattice leading to the excitation of individual, predominantly transverse NNMs, whereas the second case gives rise to nonreciprocal acoutics by considering the response of the lattice to spatially localized, transverse impulse or displacement excitations. We demonstrate intense and recurring energy exchanges between a directly excited NNM and other NNMs with higher wave numbers, so that nonreciprocal energy exchanges from small-to-large wave numbers are established. Moreover, we show the existence of nonreciprocal wave interaction phenomena in the form of irreversible targeted energy transfers from $L$ waves to $NL$ pulses during collisions of these two types of waves. Additional nonreciprocal acoustics are found in the form of complex “cascading processes, as well as nonreciprocal interactions between $L$ waves and stationary discrete breathers. The computational studies confirm the theoretically predicted transition of the lattice dynamics to a low-energy state of nonlinear acoustic vacum with strong nonlocality.

Using bibliometric data artificially generated through a model of citation dynamics calibrated on empirical data, we compare several indicators for the scientific impact of individual researchers. The use of such a controlled setup has the advantage of avoiding the biases present in real databases, and it allows us to assess which aspects of the model dynamics and which traits of individual researchers a particular indicator actually reflects. We find that the simple average citation count of the authored papers performs well in capturing the intrinsic scientific ability of researchers, regardless of the length of their career. On the other hand, when productivity complements ability in the evaluation process, the notorious $h$ and $g$ indices reveal their potential, yet their normalized variants do not always yield a fair comparison between researchers at different career stages. Notably, the use of logarithmic units for citation counts allows us to build simple indicators with performance equal to that of $h$ and $g$. Our analysis may provide useful hints for a proper use of bibliometric indicators. Additionally, our framework can be extended by including other aspects of the scientific production process and citation dynamics, with the potential to become a standard tool for the assessment of impact metrics.

Aggregation of nanoparticles of given size $R$ induced by addition of a polymer strongly depends on its degree of rigidity. This is shown here on a large variety of silica nanoparticle self-assemblies obtained by electrostatic complexation with carefully selected oppositely charged biopolyelectrolytes of different rigidity. The effective rigidity is quantified by the total persistence length $L_{\mathrm{T}}$ representing the sum of the intrinsic $\left(L_{\mathrm{p}}\right)$ and electrostatic $\left(L_{\mathrm{e}}\right)$ polyelectrolyte persistence length, which depends on the screening, i.e., on ionic strength due to counterions and external salt concentrations. We experimentally show that the ratio $L_{\mathrm{T}}/R$ is the main tuning parameter that controls the fractal dimension $D_{\mathrm{f}}$ of the nanoparticles’ self-assemblies, which is determined using small-angle neutron scattering: (i) For $L_{\mathrm{T}}/R<0.3$ (obtained with flexible poly-l-lysine in the presence of an excess of salt), chain flexibility promotes easy wrapping around nanoparticles in excess, hence ramified structures with $D_{\mathrm{f}}\sim 2$. (ii) For $0.3<L_{\mathrm{T}}/R\le 1$ (semiflexible chitosan or hyaluronan complexes), chain stiffness promotes the formation of one-dimensional nanorods (in excess of nanoparticles), in good agreement with computer simulations. (iii) For $L_{\mathrm{T}}/R>1,L_{\mathrm{e}}$ is strongly increased due to the absence of salt and repulsions between nanoparticles cannot be compensated for by the polyelectrolyte wrapping, which allows a spacing between nanoparticles and the formation of one-dimensional pearl necklace complexes. (iv) Finally, electrostatic screening, i.e., ionic strength, turned out to be a reliable way of controlling $D_{\mathrm{f}}$ and the phase diagram behavior. It finely tunes the short-range interparticle potential, resulting in larger fractal dimensions at higher ionic strength.

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

We propose an efficient Monte Carlo method for the computation of the volumes of high-dimensional bodies with arbitrary shape. We start with a region of known volume within the interior of the manifold and then use the multistate Bennett acceptance-ratio method to compute the dimensionless free-energy difference between a series of equilibrium simulations performed within this object. The method produces results that are in excellent agreement with thermodynamic integration, as well as a direct estimate of the associated statistical uncertainties. The histogram method also allows us to directly obtain an estimate of the interior radial probability density profile, thus yielding useful insight into the structural properties of such a high-dimensional body. We illustrate the method by analyzing the effect of structural disorder on the basins of attraction of mechanically stable packings of soft repulsive spheres.

A quantum thermodynamic cycle with a chiral multiferroic working substance such as ${\mathrm{LiCu}}_2{\mathrm{O}}_2$ is presented. Shortcuts to adiabaticity are employed to achieve an efficient, finite-time quantum thermodynamic cycle, which is found to depend on the spin ordering. The emergent electric polarization associated with the chiral spin order, i.e., the magnetoelectric coupling, renders possible steering of the spin order by an external electric field and hence renders possible an electric-field control of the cycle. Due to the intrinsic coupling between the spin and the electric polarization, the cycle performs an electromagnetic work. We determine this work's mean-square fluctuations, the irreversible work, and the output power of the cycle. We observe that the work mean-square fluctuations are increased with the duration of the adiabatic strokes, while the irreversible work and the output power of the cycle show a nonmonotonic behavior. In particular, the irreversible work vanishes at the end of the quantum adiabatic strokes. This fact confirms that the cycle is reversible. Our theoretical findings evidence the existence of a system inherent maximal output power. By implementing a Lindblad master equation we quantify the role of thermal relaxations on the cycle efficiency. We also discuss the role of entanglement encoded in the noncollinear spin order as a resource to affect the quantum thermodynamic cycle.

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

We present a classical, mesoscopic derivation of the Fokker-Planck equation for diffusion in an expanding medium. To this end, we take a conveniently generalized Chapman-Kolmogorov equation as the starting point. We obtain an analytical expression for the Green's function (propagator) and investigate both analytically and numerically how this function and the associated moments behave. We also study first-passage properties in expanding hyperspherical geometries. We show that in all cases the behavior is determined to a great extent by the so-called Brownian conformal time $\tau \left(t\right)$, which we define via the relation $\dot{\tau }=1/a^2$, where $a\left(t\right)$ is the expansion scale factor. If the medium expansion is driven by a power law $[a\left(t\right)\propto t^{\gamma }$ with $\gamma >0]$, then we find interesting crossover effects in the mixing effectiveness of the diffusion process when the characteristic exponent $\gamma$ is varied. Crossover effects are also found at the level of the survival probability and of the moments of the first passage-time distribution with two different regimes separated by the critical value $\gamma =1/2$. The case of an exponential scale factor is analyzed separately both for expanding and contracting media. In the latter situation, a stationary probability distribution arises in the long-time limit.

By using a physically relevant and theory independent definition of measurement-based equilibration, we show quantitatively that equilibration is easier for quantum systems than for classical systems, in the situation where the initial state of the system is completely known (a pure state). This shows that quantum equilibration is a fundamental aspect of many quantum systems, while classical equilibration relies on experimental ignorance. When the state is not completely known (a mixed state), this framework also shows that quantum equilibration requires weaker conditions.

We discuss the behavior of solitary wave solutions of the nonlinear Schrödinger equation (NLSE) as they interact with complex potentials, using a four-parameter variational approximation based on a dissipation functional formulation of the dynamics. We concentrate on spatially periodic potentials with the periods of the real and imaginary part being either the same or different. Our results for the time evolution of the collective coordinates of our variational ansatz are in good agreement with direct numerical simulation of the NLSE. We compare our method with a collective coordinate approach of Kominis and give examples where the two methods give qualitatively different answers. In our variational approach, we are able to give analytic results for the small oscillation frequency of the solitary wave oscillating parameters which agree with the numerical solution of the collective coordinate equations. We also verify that instabilities set in when the slope $dp\left(t\right)/dv\left(t\right)$ becomes negative when plotted parametrically as a function of time, where $p\left(t\right)$ is the momentum of the solitary wave and $v\left(t\right)$ the velocity.

We use the linear threshold model to study the diffusion of information on a network generated by the stochastic block model. We focus our analysis on a two-community structure where the initial set of informed nodes lies only in one of the two communities and we look for optimal network structures, i.e., those maximizing the asymptotic extent of the diffusion. We find that, constraining the mean degree and the fraction of initially informed nodes, the optimal structure can be assortative (modular), core-periphery, or even disassortative. We then look for minimal cost structures, i.e., those for which a minimal fraction of initially informed nodes is needed to trigger a global cascade. We find that the optimal networks are assortative but with a structure very close to a core-periphery graph, i.e., a very dense community linked to a much more sparsely connected periphery.

Characterizing inhomogeneous temporal patterns in natural and social phenomena is important to understand underlying mechanisms behind such complex systems and, hence, even to predict and control them. Temporal inhomogeneities in event sequences have been described in terms of bursts that are rapidly occurring events in short time periods alternating with long inactive periods. The bursts can be quantified by a simple measure, called the burstiness parameter, which was introduced by Goh and Barabási [Europhys. Lett. 81, 48002 (2008)]. The burstiness parameter has been widely used due to its simplicity, which, however, turns out to be strongly affected by the finite number of events in the time series. As the finite-size effects on burstiness parameter have been largely ignored, we analytically investigate the finite-size effects of the burstiness parameter. Then we suggest an alternative definition of burstiness that is free from finite-size effects and yet simple. Using our alternative burstiness measure, one can distinguish the finite-size effects from the intrinsic bursty properties in the time series. We also demonstrate the advantages of our burstiness measure by analyzing empirical data sets.

The shock waves generated by a plate impact are numerically investigated in Al-W laminates with different mesostructures. The main characteristic time scales (and the corresponding spatial scales) related to the formation of the stationary shock are identified: the duration (width) of the leading front, the time (distance) from the impact required to establish a stationary profile, and the shock front width, identified as a time span (distance) from the initial state to the final quasiequilibrium state. It is demonstrated that the width of the leading front and the maximum strain rates are determined by the dispersive and the nonlinear parameters of the laminate and not by the dissipation, as is the case for uniform solids. The characteristic spatial scale of the leading front is related to the spatial scale observed on solitarylike waves, which are satisfactorily described by the Korteweg–de Vries (KdV) approximation, as well as the speed of the wave and the ratio of maximum to final strain. The dissipation affects the width of the transition distance (shock front width) where multiple loading-unloading cycles bring the laminate into the final quasiequilibrium state. This spatial scale is of the same order of magnitude as the distance to form stationary shock wave. The period of fast decaying oscillations is well described by the KdV approach and scales linearly with the cell size. The rate of the decay of the oscillations in the numerical calculations does not scale with the square of the cell size as expected from the dissipative KdV approach that assumes a constant viscosity. This is due to the different mechanisms of dissipation in high-amplitude compression pulses.

Based on the linear response theory, we propose a resonance phonon (r-ph) approach to study the renormalized phonons in a few one-dimensional nonlinear lattices. Compared with the existing anharmonic phonon (a-ph) approach, the dispersion relations derived from this approach agree with the expectations of the effective phonon (e-ph) theory much better. The application is also largely extended, i.e., it is applicable in many extreme situations, e.g., high frequency, high temperature, etc., where the existing one can hardly work. Furthermore, two separated phonon branches (one acoustic and one optical) with a clear gap in between can be observed by the r-ph approach in a diatomic anharmonic lattice. While only one combined branch can be detected in the same lattice with both the a-ph approach and the e-ph theory.

An x-ray scattering approach to determine the two-dimensional (2D) pair distribution function (PDF) in partially ordered 2D systems is proposed. We derive relations between the structure factor and PDF that enable quantitative studies of positional and bond-orientational (BO) order in real space. We apply this approach in the x-ray study of a liquid crystal (LC) film undergoing the smectic-$A$-hexatic-$B$ phase transition, to analyze the interplay between the positional and BO order during the temperature evolution of the LC film. We analyze the positional correlation length in different directions in real space.

The time-dependent WKB approximation for a coherent state is expanded to third order around a guiding real trajectory, allowing for the novel treatment of nonlinearity in its semiclassical dynamics, which is generally present in all physical systems far from the classical regime. The result is a closed-form solution consisting of a linear combination of Airy functions and their derivatives multiplied by an exponential. The expression's ability to capture nonlinearity is demonstrated by examining the autocorrelation of initial coherent states in anharmonic systems with few to many contributing periodic orbits. Its accuracy is compared to the quadratic expansion and found to be superior in regimes of $\hslash$ where the curvature begins to be significant, as expected. Moreover, the expression is shown to be a real-trajectory uniformization over two coalescing saddle points that are emblematic of significant curvature. This extends real-trajectory time-dependent wave-packet semiclassical methods to highly anharmonic systems for the first time and establishes their regime of validity.

Drawing upon the bursting mechanism in slow-fast systems, we propose indicators for the prediction of such rare extreme events which do not require a priori known slow and fast coordinates. The indicators are associated with functionals defined in terms of optimally time-dependent (OTD) modes. One such functional has the form of the largest eigenvalue of the symmetric part of the linearized dynamics reduced to these modes. In contrast to other choices of subspaces, the proposed modes are flow invariant and therefore a projection onto them is dynamically meaningful. We illustrate the application of these indicators on three examples: a prototype low-dimensional model, a body-forced turbulent fluid flow, and a unidirectional model of nonlinear water waves. We use Bayesian statistics to quantify the predictive power of the proposed indicators.

Some real-world networks are shown to be fractal or self-similar. It is widespread that such a phenomenon originates from the repulsion between hubs or disassortativity. Here we show that this common belief fails to capture the causality. Our key insight to address it is to pinpoint links critical to fractality. Those links with small edge betweenness centrality (BC) constitute a special architecture called fractal reference system, which gives birth to the fractal structure of those reported networks. In contrast, a small amount of links with high BC enable small-world effects, hiding the intrinsic fractality. With enough of such links removed, fractal scaling spontaneously arises from nonfractal networks. Our results provide a multiple-scale view on the structure and dynamics and place fractality as a generic organizing principle of complex networks on a firmer ground.

Spontaneous calcium (Ca) waves in cardiac myocytes are known to underlie a wide range of cardiac arrhythmias. However, it is not understood which physiological parameters determine the onset of waves. In this study, we explore the relationship between Ca signaling between ion channels and the nucleation of Ca waves. In particular, we apply a master equation approach to analyze the stochastic interaction between neighboring clusters of ryanodine receptor (RyR) channels. Using this analysis, we show that signaling between clusters can be described as a barrier hopping process with exponential sensitivity to system parameters. A consequence of this feature is that the probability that Ca release at a cluster induces release at a neighboring cluster exhibits a sigmoid dependence on the Ca content in the cell. This nonlinearity originates from the regulation of RyR opening due to more than one Ca ion binding site, in conjunction with Ca mediated cooperativity between RyR channels in clusters. We apply a spatially distributed stochastic model of Ca cycling to analyze the physiological consequences of this nonlinearity, and show that it explains the sharp onset of Ca wave nucleation in cardiac cells. Furthermore, we show that this sharp onset can serve as a mechanism for Ca alternans under physiologically relevant conditions. Thus our findings identify the nonlinear features of Ca signaling which potentially underlie the onset of Ca waves and Ca alternans in cardiac cells.