We perform molecular dynamics simulations of liquid water at different temperatures and calculate the water viscosity, the translational and rotational water diffusivities in the laboratory frame as well as in the comoving molecular frame. Instead of interpreting the results as deviations from the Stokes-Einstein and Stokes-Einstein-Debye relations, we describe the translational and rotational diffusivities of water molecules by three models of increasing complexity that take the structural anisotropy of water into account on different levels. We first compare simulation results to analytical predictions for a no-slip sphere and a no-slip ellipsoid. We show that the no-slip sphere can approximate laboratory-frame isotropic translational and rotational diffusivities but fails to describe the anisotropic molecular-frame diffusivities. The no-slip ellipsoid can describe the translational anisotropic molecular-frame diffusivities exactly but fails to describe the translational and rotational anisotropic molecular-frame diffusivities simultaneously. Since an ellipsoidal model with slip boundary conditions is not analytically tractable, we define a heuristic spherical model with tensorial slip lengths and tensorial hydrodynamic radii. We show that this model simultaneously describes the laboratory-frame isotropic translational and rotational diffusivities, as well as, in a restricted viscosity range, the anisotropic molecular-frame diffusivities.

Based on a nonlinear extension of the Ericksen-Leslie theory, taking into account the entropy balance equation, a theoretical study of a thermally excited vortex flow in a microsized hybrid-aligned nematic (HAN) volume was carried out. Analysis of the numerical results show that due to interaction between the gradients of the director field $\mathbf{\nabla }\widehat{\mathbf{\text{n}}}$ and temperature $\mathbf{\nabla }T$, caused by the focused laser radiation, the thermally excited vortical fluid flow is maintained in the bulk of the HAN channel. Calculations have shown that the features of the vortex flow are influenced not only by the direction of the heat flux relative to the bounding surfaces, but also by the orientational defect on these surfaces.

We consider the random deposition of objects of variable width and height over a line. The successive additions of these structures create a random interface. We focus on the regime of heavy-tailed distributions of the structure width. When the structure center is chosen at random, the problem is exactly solvable, and the interface generically tends toward a self-affine random curve. The asymptotic behavior reached after a large number of iterations is universal in the sense that it depends on only three parameters: the shape of the added structure at its maximum, the power-law exponent of the width distribution, and the exponent that relates height and width. The parameter space displays several transitions that separate different asymptotic behaviors. In particular, for a set of parameters, the interface tends toward a fractional Brownian motion. Our results reveal the existence of a new class of random interfaces whose properties appear to be robust. The mechanism that generates correlations at large distances is identified, and it explains the appearance of such correlations in several situations of interest, such as the physics of earthquakes or the propagation of energy through a diffusive medium.

Reliability and accuracy of lateral correlation length measurements are studied and quantified from the analysis of synthetic correlated profiles. First, we review available methods to characterize self-affine profiles; we discuss the autocorrelation, Hurst, interface width, and maximum difference functions as widely applicable. We demonstrate that the functions are essentially related and give comparable predictions of the scaling behavior. Second, we consider definitions of correlation length employed in practice. Roughly, they might be cast into two groups, selecting by whether they do not require or require fitting. Approaches from the first group are straightforward and easy to implement; however, they may over- or underestimate the value of correlation length on a small data set due to a size effect. Approaches from the second group may smooth possible oscillations; nevertheless, their precision highly depends on the fit quality. We demonstrate that correlation length found with different approaches might be easily rescaled one onto another. In addition, we introduce a parameter which is further used to estimate accuracy of measurements. Third, we estimate accuracy of all functions and methods on synthetic correlated profiles. We demonstrate influence of the size effect on statistical functions. We show that different methods have different accuracy and different convergence rate to the true value. Fourth, we estimate a parameter saying how much profile length should be larger than the measured value of correlation length in order to get the desirable accuracy of measurements. Finally, we conclude our paper with the recommendation to define correlation length as an abscissa of the $e^{-1}$ point of the autocorrelation function, and note that the accuracy of $10\%$ is achieved if 100 studied profiles are at least 50 times larger than the measured value of correlation length.

In a specific class of open quantum systems with finite and fixed numbers of collapsed quantum states, the semi-Markov process method is used to calculate the large deviations of the first passage time statistics. The core formula is an equation of poles, which is also applied in determining the scaled generating functions (SCGFs) of the counting statistics. For simple counting variables, the SCGFs of the first passage time statistics are derived by finding the largest modulus of the roots of this equation with respect to the $z$-transform parameter and then calculating its logarithm. The procedure is analogous to that of solving for the SCGFs of the counting statistics. However, for current-like variables, the method generally fails unless the equation of pole is simplified to a quadratic form. The fundamental reason for this lies in the nonuniqueness between the roots and the region of convergence for the joint transform. We illustrate these results via a resonantly driven two-level quantum system, where for several counting variables the solutions to the SCGFs of the first passage time are analytically obtained. Furthermore, we apply these functions to investigate quantum violations of the classical kinetic and thermodynamic uncertainty relations.

We present a Brownian dynamics simulation of the bacterial Stirling engine studied by Krishnamurthy et al. [Nat. Phys. 12, 1134 (2016)]. In their experimental setup, an overdamped colloid in an optical trap with time-modulated stiffness interacts with a bacterial bath that we represent by an ensemble of overdamped active particles. In the parameter regime of the experiment the thermodynamic performance is governed by an effective temperature and can be parametrized analytically by active Brownian particle models. We quantitatively reproduce the efficiencies reported for the experiments under the assumption that energy exchange with the bath during isochores of the cycle is entirely recuperated and in agreement with the second law.

We use Brownian dynamics simulations to study a model of a cyclic bacterial heat engine based on a harmonically confined colloidal probe particle in a bath formed by active Brownian particles. For intermediate activities, active noise experienced by large enough probes becomes Gaussian with exponential autocorrelation function. We show that, in this experimentally pertinent regime, the probability densities for stochastic work, heat, and efficiency are well represented by those of a single active Ornstein-Uhlenbeck particle (AOUP), effectively representing the whole many-body setup. Due to the probe's fast relaxation in the potential, in typical experimental implementations, good agreement can prevail even when the autocorrelation function of the active noise develops nonexponential tails. Our results show that the AOUP provides a convenient and accurate, analytically tractable effective model to mimic and analyze experimental bacterial heat engines, especially when operating with comparatively large probes and stiff traps.

Obtaining the low-energy configurations of spin glasses that have rugged energy landscapes is of direct relevance to combinatorial optimization and fundamental science. Search-based heuristics have difficulty with this task due to the existence of many local minima that are far from optimal. The work of M. M. Rams et al. [Phys. Rev. E 104, 025308 (2021)] demonstrates an alternative that can bypass this issue for spin glasses with planar or quasiplanar geometry: sampling the Boltzmann distribution via approximate contractions of tensor networks. The computational complexity of this approach is due only to the complexity of contracting the network and is therefore independent of landscape ruggedness. Here we initiate an investigation of how to take this approach beyond (quasi-)planar geometry by utilizing hyperoptimized approximate contraction of tensor networks [J. Gray and G. K.-L. Chan, Phys. Rev. X 14, 011009 (2024)]. We perform tests on the periodic square- and cubic-lattice, planted-solution Ising spin glasses generated with tile planting [F. Hamze et al., Phys. Rev. E 97, 043303 (2018)] for up to 2304 (square lattice) and 216 (cubic lattice) spins. For a fixed bond dimension, the time complexity is quadratic. With a bond dimension of only four, over the tested system sizes, the average relative energy error in the most rugged instance class remains $\sim 1\%$ (square lattice) or $\sim 10\%$ (cubic lattice) of optimal. In less rugged instances the solution is always optimal for the square lattice and either optimal or within $\sim 1\%$ for the cubic lattice. These results suggest that further development of optimization methods based on tensor-network representations of spin glass partition functions may be fruitful, especially given that such methods are not limited to the Ising (i.e., binary) or two-body (i.e., quadratic) settings.

Field-theoretical calculations predict that, at the upper critical dimension $d_c=4$, the finite-size scaling (FSS) behaviors of the Ising model would be modified by multiplicative logarithmic corrections with thermal and magnetic correction exponents $({\widehat{y}}_t,{\widehat{y}}_h)=(1/6,1/4)$. Using high-efficient cluster algorithms and the lifted worm algorithm, we present a systematic study to the FSS of the four-dimensional Ising model at criticality in the Fortuin-Kasteleyn (FK) bond and loop representations. In the FK representation, the size of the largest cluster is observed to scale as $C_1\sim L^3{(lnL)}^{{\widehat{y}}_h}$, while the size of the second-largest cluster scales as $C_2\sim L^3{(lnL)}^{{\widehat{y}}_{h2}}$ with ${\widehat{y}}_{h2}=-1/4$ a new correction exponent not yet predicted from field theory. In the loop representation, we observe that the size of the largest loop cluster scales as $F_1\sim L^2{(lnL)}^{{\widehat{y}}_t}$, and the specific heat scales as $c_{\mathrm{E}}\sim {(lnL)}^{2{\widehat{y}}_t}$. This clarifies the long-standing open question that whether the specific heat for the critical Ising model at $d_c=4$ diverges logarithmically.

Self-organized criticality is a dynamical system property where, without external tuning, a system naturally evolves towards its critical state, characterized by scale-invariant patterns and power-law distributions. In this paper, we explored a self-organized critical dynamic on the Sierpinski carpet lattice, a scale-invariant structure whose dimension is defined as a power law with a noninteger exponent, i.e., a fractal. To achieve this, we proposed an Ising–bond-correlated percolation model as the foundation for investigating critical dynamics. Within this framework, we outlined a feedback mechanism for critical self-organization and followed an algorithm for its numerical implementation. The results obtained from the algorithm demonstrated enhanced efficiency when driving the Sierpinski carpet towards critical self-organization compared to a two-dimensional lattice. This efficiency was attributed to the iterative construction of the lattice and the distribution of spins within it. The key outcome of our findings is a dependence of self-organized criticality on topology for this particular model, which may have several applications in fields regarding information transmission.

Lithium-ion batteries charge and discharge via ion intercalation reactions that store and release energy in evolving electrochemically active regions. In common electrode materials which consist of phase-separating nanoparticles, such as lithium iron phosphate (LFP) and graphite, this process often results in heterogeneous “mosaic” patterns with evolving populations of nearly homogeneous particles. These electrode-scale heterogeneities create hotspots in current and temperature, which can drive degradation by side reactions or mechanical deformation. While mosaic phase separation has been observed experimentally using x-ray or optical microscopy, and computationally in simulations using multiphase porous electrode theory (MPET), there is still no mathematical theory to predict the relevant time scales and active population dynamics. Here, starting from a single-particle conservation equation, we develop a population scale model and use eigendecompositions to predict the transition between a stochastic regime in the spinodal gap to a deterministic regime in the solid solution regime. In the stochastic regime, a strong asymmetry in timescales is observed driven by the single-particle instability at the barrier maxima, which is validated by MPET simulations and experimental data. This transition occurs based on the predicted nonequilibrium free energy barrier, which arises from competition between process and reaction timescales of population dynamics. The theory predicts charge/discharge asymmetries in the active particle fraction due to autocatalysis at the population scale, consistent with experiments and simulations [Y. Li et al., Nat. Mater. 13, 1149 (2014), K. Xiang et al., Chem. Mater. 30, 4216 (2018)].

This paper explores the conditions under which global contraction manifests in the leaky continuous time reservoirs, thus guaranteeing generalized synchronization. Results on continuous time reservoirs make use of the logarithmic norm of the connectivity matrix. Further analysis yields some simple guidelines on how to better construct the connectivity matrix in these systems. Additionally, we outline how the universal approximation property of discrete time reservoirs is readily satisfied by virtue of the activation function being contracting, and how continuous time reservoirs may inherit a limited form of universal approximation by virtue of them overlapping with neural ordinary differential equations. The ability of the reservoir computing framework to universally approximate topological conjugates, along with their fast training, make them a compelling data-driven, black-box surrogate of dynamical systems and a potential candidate for a component of digital twins.

In the context of non-Hermitian photonics, we consider a nonlinear optical trimer with three lossy waveguides with complex couplings. This non-Hermitian trimer exhibits stable stationary and oscillatory regimes in a wide range of values of the coupling-loss parameters. Moreover, chaotic dynamics through period doubling is confirmed via Lyapunov exponent measurements and the underlying bifurcation structure is found by semianalytical continuation of solutions. The interplay of chaos, due to Kerr nonlinearity, and non-Hermiticity, due to the combined dissipation and complex coupling, provides a different perspective in the area of nonlinear and non-Hermitian optics.

Coupled oscillator models are of fundamental importance for understanding the collective dynamics that underlie many realistic applications ranging from physics and biology to human society. Here, we investigate the dynamics of oscillation quenching in a system of globally coupled Stuart-Landau limit-cycle oscillators incorporating the random heterogeneous interactions. We aim to provide a generic approach to systematically comprehending stability properties, as well as to appreciating the underlying emergent mechanism, of the quenching dynamics under the impression of inhomogeneous couplings. Importantly, we uncover that the peculiar symmetry of the linearized system profoundly facilitates the analysis of the algebraic structures of the eigenspectrum, thereby reformulating the characteristic equations deciding the eigenvalues in the simple forms for both finite and infinite sizes of the coupled system. In particular, the critical conditions manifesting the onset of oscillation quenching can be analytically characterized in terms of the matrix theory with finite-rank perturbation. Our work, thus, is capable of providing insights for controlling and regulating the oscillatory dynamics in complex systems consisting of interacting agents with large degrees of freedom.

We develop a hypothesis that the dynamics of equilibrium systems at criticality have their dynamics constricted to a fractal subspace. We relate the correlation fractal dimension associated with this subspace to the Fisher critical exponent controlling the singularity associated with the correlation function. This fractal subspace is different from that associated with the order parameter. We propose a relation between the correlation fractal dimension and the order parameter fractal dimension. The fractal subspace we identify has as a defining property that the correlation function is restored at the critical point by restricting the dynamics this way. We determine the correlation fractal dimension of the two-dimensional Ising model and validate it by computer simulations. We discuss growth models briefly in this context.