We study the collective vibrational excitations of crystals under out-of-equilibrium steady conditions that give rise to entropy production. Their excitation spectrum comprises equilibriumlike phonons of thermal origin and additional collective excitations called entropons because each of them represents a mode of spectral entropy production. Entropons coexist with phonons and dominate them when the system is far from equilibrium while they are negligible in near-equilibrium regimes. The concept of entropons has been recently introduced and verified in a special case of crystals formed by self-propelled particles. Here we show that entropons exist in a broader class of active crystals that are intrinsically out of equilibrium and characterized by the lack of detailed balance. After a general derivation, several explicit examples are discussed, including crystals consisting of particles with alignment interactions and frictional contact forces.

We study the finite-temperature dynamics of thin elastic sheets in a single-clamped cantilever configuration. This system is known to exhibit a tilt transition at which the preferred mean plane of the sheet shifts from horizontal to a plane above or below the horizontal. The resultant thermally roughened two-state (up/down) system possesses rich dynamics on multiple timescales. In the tilted regime a finite-energy barrier separates the spontaneously chosen up state from the inversion-symmetric down state. Molecular dynamics simulations confirm that, over sufficiently long time, such thermalized elastic sheets transition between the two states, residing in each for a finite dwell time. One might expect that temperature is the primary driver for tilt inversion. We find, instead, that the primary control parameter, at fixed tilt order parameter, is the dimensionless and purely geometrical aspect ratio of the clamped width to the total length of the otherwise-free sheet. Using a combination of an effective mean-field theory and Kramers' theory, we derive the transition rate and examine its asymptotic behavior. At length scales beyond a material-dependent thermal length scale, renormalization of the elastic constants qualitatively modifies the temperature response. In particular, the transition is suppressed by thermal fluctuations, enhancing the robustness of the tilted state. We check and supplement these findings with further molecular dynamics simulations for a range of aspect ratios and temperatures.

The computational and theoretical analysis carried out in this article demonstrates the existence of a nontrivial mechanism for the compression of a submicron-sized gas bubble formed by a gas of classical ions and a gas of degenerate electrons. This mechanism fundamentally differs from conventional compression mechanisms. It is shown that taking into account the quantum effect of a large spatial scale in the distribution of electrons qualitatively changes the character of cumulative processes. Because of a large-scale electric field caused by quantum shell effects, the compression process is characterized by the formation of multiple shock waves. The values of gas temperature and pressure achieved during compression occur higher by two orders of magnitude as compared with the classical adiabatic regime. The analysis is carried out within the framework of the following model: the dynamics of the electron subsystem is described by equations of a quantum electron fluid, while the hydrodynamic approximation is adopted for the ionic subsystem. The large-scale effect is taken into account by means of effective external field acting on electrons. The theoretical analysis carried out within this approach clarifies the nature of the cumulative process in the system under consideration; some quantitative characteristics obtained with numerical simulation are presented. The possibility of experimental observation of this cumulative mechanism is analyzed. It is suggested that the manifestation of the effect can be observed during laser compression of a system of submicron targets by measuring the neutron yield.

We introduce a general, variational scheme for systematic approximation of a given Kohn-Sham free-energy functional by partitioning the density matrix into distinct spectral domains, each of which may be spanned by an independent diagonal representation without requirement of mutual orthogonality. It is shown that by generalizing the entropic contribution to the free energy to allow for independent representations in each spectral domain, the free energy becomes an upper bound to the exact (unpartitioned) Kohn-Sham free energy, attaining this limit as the representations approach Kohn-Sham eigenfunctions. A numerical procedure is devised for calculation of the generalized entropy associated with spectral partitioning of the density matrix. The result is a powerful framework for Kohn-Sham calculations of systems whose occupied subspaces span multiple energy regimes. As a case in point, we apply the proposed framework to warm- and hot-dense matter described by finite-temperature density functional theory, where at high energies the density matrix is represented by that of the free-electron gas, while at low energies it is variationally optimized. We derive expressions for the spectral-partitioned Kohn-Sham Hamiltonian, atomic forces, and macroscopic stresses within the projector-augmented wave (PAW) and the norm-conserving pseudopotential methods. It is demonstrated that at high temperatures, spectral partitioning facilitates accurate calculations at dramatically reduced computational cost. Moreover, as temperature is increased, fewer exact Kohn-Sham states are required for a given accuracy, leading to further reductions in computational cost. Finally, it is shown that standard multiprojector expansions of electronic orbitals within atomic spheres in the PAW method lack sufficient completeness at high temperatures. Spectral partitioning provides a systematic solution for this fundamental problem.

We investigate a simple network, which has a branching-merging structure, using the totally asymmetric simple exclusion process, considering conflicts at the merging point. For both periodic and open boundary conditions, the system exhibits metastability. Specifically, for open boundary conditions, we observe two types of metastability: hysteresis and a nonergodic phase. We analytically determine the tipping points, that is, the critical conditions under which a small disturbance can lead to the collapse of metastability. Our findings provide insights into metastability induced by branching-merging structures, which exist in all network systems in various fields.

Since the early 1970s, numerous systems exhibiting an algebraic structure resembling that of the 1963 Lorenz system have been proposed. These systems have occasionally yielded the same attractor as the Lorenz system, while in other cases, they have not. Conversely, some systems that are evidently distinct from the Lorenz system, particularly in terms of symmetry, have resulted in attractors that bear a resemblance to the Lorenz attractor. In this paper, we put forward a definition for Lorenz-like systems and Lorenz-like attractors. The former definition is based on the algebraic structure of the governing equations, while the latter relies on topological characterization. Our analysis encompasses over 20 explicitly examined chaotic systems.

Classical percolation theory underlies many processes of information transfer along the links of a network. In these standard situations, the requirement for two nodes to be able to communicate is the presence of at least one uninterrupted path of nodes between them. In a variety of more recent data transmission protocols, such as the communication of noisy data via error-correcting repeaters, both in classical and quantum networks, the requirement of an uninterrupted path is too strict: two nodes may be able to communicate even if all paths between them have interruptions or gaps consisting of nodes that may corrupt the message. In such a case a different approach is needed. We develop the theoretical framework for extended-range percolation in networks, describing the fundamental connectivity properties relevant to such models of information transfer. We obtain exact results, for any range $R$, for infinite random uncorrelated networks and we provide a message-passing formulation that works well in sparse real-world networks. The interplay of the extended range and heterogeneity leads to novel critical behavior in scale-free networks.

We report the stability of a falling incompressible odd viscosity fluid on flexible substrates when the time-reversal symmetry is broken. The flexible wall equation incorporates the contribution of odd viscosity, where the stress at an interface is determined by the viscosities of the adjacent fluids. The Orr-Sommerfeld (OS) equation is derived using the modified linear flexible wall equation taking the inertia, flexural rigidity, and spring stiffness effects of the elastic plate into account. Here, we solve the above eigenvalue problem using Chebyshev collocation methods to obtain the neutral curve in the $k$-Re plane and the temporal growth rate under varying values of odd viscosity. There is an interesting finding that, for moderate Reynolds numbers, the presence of odd viscosity leads to an increase in instability when the stiffness coefficient $A_K$ is small. However, as the value of the stiffness coefficient $A_K$ rises, the effect of odd viscosity changes to suppress the onset of instability. Additionally, at higher Reynolds numbers and extremely small inclination angles, both shear and wall modes of falling film are observed. The results demonstrate that the unstable domain for the wall mode increases as the odd viscosity coefficient value rises, while an opposite trend occurs in the shear mode.

We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position $x_0$ $(>0)$. By deriving the exit probability of RBM in an interval $[0,M]$ from the origin, we obtain the distribution $P_r\left(M\right|x_0)$ of the maximum displacement $M$ and thus gives the expected value $\langle M\rangle$ of $M$ as functions of the resetting rate $r$ and $x_0$. We find that $\langle M\rangle$ decreases monotonically as $r$ increases, and tends to $2x_0$ as $r\to \infty$. In the opposite limit, $\langle M\rangle$ diverges logarithmically as $r\to 0$. Moreover, we derive the propagator of RBM in the Laplace domain in the presence of both absorbing ends, and then leads to the joint distribution $P_r(M,t_m|x_0)$ of $M$ and the time $t_m$ at which this maximum is achieved in the Laplace domain by using a path decomposition technique, from which the expected value $\langle t_m\rangle$ of $t_m$ is obtained explicitly. Interestingly, $\langle t_m\rangle$ shows a nonmonotonic dependence on $r$, and attains its minimum at an optimal $r^{*}\approx 2.71691D/x_0^2$, where $D$ is the diffusion coefficient. Finally, we perform extensive simulations to validate our theoretical results.

Since the times of Holtsmark (1911), statistics of fields in random environments have been widely studied, for example in astrophysics, active matter, and line-shape broadening. The power-law decay of the two-body interaction of the form $1/{\left|r\right|}^{\delta }$, and assuming spatial uniformity of the medium particles exerting the forces, imply that the fields are fat-tailed distributed, and in general are described by stable Lévy distributions. With this widely used framework, the variance of the field diverges, which is nonphysical, due to finite size cutoffs. We find a complementary statistical law to the Lévy-Holtsmark distribution describing the large fields in the problem, which is related to the finite size of the tracer particle. We discover biscaling with a sharp statistical transition of the force moments taking place when the order of the moment is $d/\delta$, where $d$ is the dimension. The high-order moments, including the variance, are described by the framework presented in this paper, which is expected to hold for many systems. The new scaling solution found here is nonnormalized similar to infinite invariant densities found in dynamical systems.

Resetting is a strategy for boosting the speed of a target-searching process. Since its introduction over a decade ago, most studies have been carried out under the assumption that resetting takes place instantaneously. However, due to its irreversible nature, resetting processes incur a thermodynamic cost, which becomes infinite in the case of instantaneous resetting. Here, we take into consideration both the cost and the first passage time (FPT) required for a resetting process, in which the reset or return to the initial location is implemented using a trapping potential over a finite but random time period. An iterative generating function and a counting functional method à la Feynman and Kac are employed to calculate the FPT and the average work for this process. From these results, we obtain an explicit form of the time-cost trade-off relation, which provides the lower bound of the mean FPT for a given work input when the trapping potential is linear. This trade-off relation clearly shows that instantaneous resetting is achievable only when an infinite amount of work is provided. More surprisingly, the trade-off relation derived from the linear potential seems to be valid for a wide range of trapping potentials. In addition, we have also shown that the fixed-time or sharp resetting can further enhance the trade-off relation compared to that of the stochastic resetting.

Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the active vertex model exist and yield reasonable agreement with experimental observations such as tissue fluidization or fingering. However, a good and well-founded continuum description for tissues remains to be developed. In this work, we derive a macroscopic description for a two-dimensional cell monolayer by coarse-graining the vertex model through the Poisson bracket approach. We obtain equations for cell density, velocity, and the cellular shape tensor. We then study the homogeneous steady states, their stability (which coincides with thermodynamic stability), and especially their behavior under an externally applied shear. Our results contribute to elucidate the interplay between flow and cellular shape. The obtained macroscopic equations present a good starting point for adding cell motion, morphogenetic, and other biologically relevant processes.

We investigate analytically and numerically a system of clusters evolving via collisions with clusters of minimal mass (monomers). Each collision either leads to the addition of the monomer to the cluster or the chipping of a monomer from the cluster, and emerging behaviors depend on which of the two processes is more probable. If addition prevails, monomers disappear in a time that scales as $lnN$ with the total mass $N\gg 1$, and the system reaches a jammed state. When chipping prevails, the system remains in a quasistationary state for a time that scales exponentially with $N$, but eventually, a giant fluctuation leads to the disappearance of monomers. In the marginal case, monomers disappear in a time that scales linearly with $N$, and the final supercluster state is a peculiar jammed state; i.e., it is not extensive.

The nonequilibrium steady state emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution of resetting positions. The coefficients of this series are universal in the sense that they do not depend on the resetting distribution, only the underlying dynamics. We consider the case of a Brownian particle and a run-and-tumble particle confined in a harmonic potential, where we derive explicit closed-form expressions for all moments for any resetting distribution. Numerical simulations are used to verify the results, showing excellent agreement.

Quantum directed transport can be realized in noninteracting, deterministic, chaotic systems by appropriately breaking the spatiotemporal symmetries in the potential. In this work, the focus is on the class of interacting two-body quantum systems whose classical limit is chaotic. It is shown that one subsystem effectively acts as a source of “noise” to the other leading to intrinsic temporal symmetry breaking. Then, the quantum directed currents, even if prohibited by symmetries in the composite system, can be realized in the subsystems. This current is of quantum origin and does not arise from semiclassical effects. This protocol provides a minimal framework—broken spatial symmetry in the potential and presence of interactions—for realizing directed transport in interacting chaotic systems. It is also shown that the magnitude of directed current undergoes multiple current reversals upon varying the interaction strength and this allows for controlling the currents. It is explicitly demonstrated in the two-body interacting kicked rotor model. The interaction-induced mechanism for subsystem directed currents would be applicable to other interacting quantum systems as well.

Translation is one of the most fundamental processes in the biological cell. Because of the central role that translation plays across all domains of life, the enzyme that carries out this process, the ribosome, is required to process information with high accuracy. This accuracy often approaches values near unity experimentally. In this paper, we model the ribosome as an information channel and demonstrate mathematically that this biological machine has information-processing capabilities that have not been recognized previously. In particular, we calculate bounds on the ribosome's theoretical Shannon capacity and numerically approximate this capacity. Finally, by incorporating estimates on the ribosome's operation time, we show that the ribosome operates at speeds safely below its capacity, allowing the ribosome to process information with an arbitrary degree of error. Our results show that the ribosome achieves a high accuracy in line with purely information-theoretic means.

We investigate the influence of external forces on the collective dynamics of interacting active Brownian particles in two as well as three spatial dimensions. Via explicit coarse graining, we derive predictive models, i.e., models that give a direct relation between the models' coefficients and the bare parameters of the system, that are applicable for space- and time-dependent external force fields. We study these models for the cases of gravity and harmonic traps. In particular, we derive a generalized barometric formula for interacting active Brownian particles under gravity that is valid for low to high concentrations and activities of the particles. Furthermore, we show that one can use an external harmonic trap to induce motility-induced phase separation in systems that, without external fields, remain in a homogeneous state. This finding makes it possible to realize programmable density patterns in systems of active Brownian particles. Our analytic predictions are found to be in very good agreement with Brownian dynamics simulations.

We employ only the positions of colloidal particles and construct machine learning (ML) models to test the presence of structural order in glass transition for two kinds of two-dimensional (2D) colloids: 2D polydisperse colloids (PC) with medium-range crystalline order (MRCO) and 2D binary colloids (BC) without MRCO. ML models predict the glass transition of 2D colloids successfully without any information on MRCO. Even certain ML models trained with BC predict the glass transition of PC successfully, thus suggesting that universal structural characteristics would exist besides MRCO.

We obtain the von Kármán–Howarth relation for the stochastically forced three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid turbulence in helium (${}^4\mathrm{He}$) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analytical studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P\left(\gamma \right)$, of the ratio $\gamma$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P\left(\gamma \right)\sim {\gamma }^3$, for $\gamma \ll 1$, and $P\left(\gamma \right)\sim {\gamma }^{-3}$, for $\gamma \gg 1$. Furthermore, we show that the PDF $P\left(\theta \right)$ of the angle $\theta$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P\left(\theta \right)\sim \theta$ for $\theta \ll {\theta }_{*}$ and $P\left(\theta \right)\sim {\theta }^{-4}$ for ${\theta }_{*}\ll \theta \ll 1$, where ${\theta }_{*}$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, as well as the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid helium ${}^4\mathrm{He}$, so our results are of direct relevance to superfluid turbulence in this system.

The rheology of biological tissue is key to processes such as embryo development, wound healing, and cancer metastasis. Vertex models of confluent tissue monolayers have uncovered a spontaneous liquid-solid transition tuned by cell shape; and a shear-induced solidification transition of an initially liquidlike tissue. Alongside this jamming/unjamming behavior, biological tissue also displays an inherent viscoelasticity, with a slow time and rate-dependent mechanics. With this motivation, we combine simulations and continuum theory to examine the rheology of the vertex model in nonlinear shear across a full range of shear rates from quastistatic to fast, elucidating its nonlinear stress-strain curves after the inception of shear of finite rate, and its steady state flow curves of stress as a function of strain rate. We formulate a rheological constitutive model that couples cell shape to flow and captures both the tissue solid-liquid transition and its rich linear and nonlinear rheology.