Loss of hydrostaticity limits high-pressure experiments, as pressure transmitting media solidify under compression. Here, we report a strong and positive correlation between the increase of molar density with pressure ($\zeta$) and the hydrostatic limit (HL) associated with the vitrification of isothermally compressed molecular liquids. This correlation is derived using molecular dynamics simulations and is validated against experimental values of $\zeta$ and HL. The positive $\zeta$–HL correlation can be rationalized by writing $\zeta$ as a function of the molar density ($\rho$) and the pressure-induced decrease in molar volume ($\upsilon$): $\zeta ={\rho }^2\upsilon$. While liquids are seen to not exhibit large $\rho$ and $\upsilon$ simultaneously, we find that large HL values originate mostly from large $\rho$, or, to some extent, from a large $\upsilon$. At the molecular level, large $\rho$ and large $\upsilon$ are linked to small molecular sizes and to low characteristic frequencies of intermolecular vibrations ($\omega$), respectively.

Petrov [Phys. Rev. E 111, 035205 (2025)] has presented an explanation of some parameters of terrestrial gamma-ray flashes within the framework of his model which is based on the assumptions about the formation of surface plasmon waves and the generation of synchrotron radiation due to the interaction of these waves with the electric field associated with the lightning channel. Here it is shown that this explanation involves the mistaken use of equations, describing the generation of synchrotron radiation by electrons. Namely, the velocity of the surface plasmon wave is substituted into these equations instead of the velocity of the electron.

We investigate a nonequilibrium steady-state model consisting of two coupled beads with arbitrary masses in contact with two thermal baths at different temperatures. Using a covariance-matrix approach together with numerical simulations of the underdamped Langevin dynamics, we characterize steady-state probability distributions, heat transport, and entropy production. We show that irreversibility measures such as entropy production and heat current are invariant under an exchange of the bead masses, whereas energy-storage observables depend explicitly on the mass arrangement in a symmetrical setup. This reveals a fundamental distinction: energy observables exhibit path dependence in singular mass limits, while transport and irreversibility remain well defined. We show that kinetic temperatures provide the natural variables governing the thermodynamics of the system: their difference controls transport and entropy production, while their sum determines the mean energy via a model-specific generalized equipartition relation. In the infinite-mass limit, only constitutive relations expressed in terms of kinetic temperatures remain meaningful. Thus, energy, transport, and irreversibility are unified through kinetic temperatures as the organizing variables. We also derive an effective temperature that defines an equilibrium-like canonical distribution. Finally, we analyze the notion of ergodicity and show that the time-averaged observables converge significantly faster than the ensemble averages.

We investigate the geometric structure of evolving infectious-disease networks using a notion of node curvature, which is based on the heat-kernel expansion that naturally extends to edges. Applying this measure to networks reconstructed from infection counts whose degree and strength distributions transition toward a steady power-law, we observe a corresponding transition in curvature. We relate the latter to an underlying hyperbolic space and reveal a phase transition in the network's effective temperature. We further compare our curvature measure with existing definitions in the literature, demonstrating that all capture the transition consistently. Our results suggest that curvature provides a metric for characterizing structural changes in dynamic networks arising from infectious processes and identifies distinct phases where targeted vaccination strategies may be most effective, when used within a multimetric public health decision-making framework.

The approximate master equation (AME) provides a highly accurate description of dynamical processes on networks, yet its steady states are generally analytically intractable. In this study, we develop an analytical framework to derive the steady states of the AME by introducing a controlled approximation that enables closure of the moment equations. This framework reproduces the steady state of the pair approximation by achieving closure with the minimum required order of moments, and can be systematically refined to approach the exact steady states of the AME. We apply this to the susceptible-infected-susceptible model, the voter model, and evolutionary games, demonstrating that the steady states can be derived. In particular, for evolutionary games, we show that combining our framework with the singular perturbation method enables the analytical derivation of the time evolution.

We investigate magnetohydrodynamic (MHD) turbulence in plane shear flows with a streamwise background magnetic field in the super-Alfvénic regime, i.e., when the flow velocity is larger than the local Alfvén speed. In this regime, turbulence is energetically supplied by large-scale shear of the flow via transient or nonmodal amplification of Alfvén waves, which are the building blocks of MHD turbulence, and streamwise-uniform, mostly nonmagnetic modes. We show that shear reduces turbulence imbalance, driving the system toward a balanced state—the energies of counter-propagating Alfvén waves become essentially equal, even for an initially perfectly imbalanced Alfvénic turbulence. This balancing occurs due to the shear-induced linear nonmodal dynamics of Alfvén waves—their nonmodal growth, resulting in over-reflection, and coupling between counterpropagating wave branches. Because of its linear origin, this process of balancing of MHD turbulence by shear is fundamentally different from the nonlinear processes operating in standard MHD turbulence in the absence of a mean shear flow. It can have direct implications for understanding the balanced/imbalanced nature of MHD turbulence in shear regions of the solar wind.

We study a quasi-one-dimensional associating fluid composed of hard superellipses carrying two patches interacting through a directional Kern-Frenkel potential. Using the transfer operator method, we show that the selective patch-patch association promotes horizontal alignment and chain formation at low-to-intermediate densities, whereas hard-core interaction favors vertical alignment without bonds at high densities. The competition between these two mechanisms drives a structural crossover upon compression from a horizontally aligned bonded chain structure to a completely unbonded, vertically aligned structure. While patchy ellipses undergo a tilted-to-vertical realignment, patchy rectangle-like superellipses exhibit a horizontal-to-vertical change. These structural changes manifest as a plateau in the equation of state. To capture these properties, we generalize Wertheim's first-order thermodynamic perturbation theory by introducing an orientation-dependent fraction of sites not in a bond. When combined with the Parsons-Lee hard-body theory, the orientationally resolved perturbation theory provides quantitatively reliable results for the structural properties and phase behavior. Therefore, the generalized Wertheim theory together with the Parsons-Lee theory can be suitable in higher dimensions, too.

Light localization can significantly enhance light-matter interactions, making it crucial for achieving low-threshold lasers. In this study, we investigate how the degree of disorder in the positions of defect layers affects the localization of defect modes in the cholesteric liquid crystal with multiple defect layers. Defect modes are inherently localized within the defect layers. But the modes exhibit an extended state throughout the periodic defect layers due to mode coupling between nearest-neighbor layers. As the degree of disorder increases, the defect-mode field redistributes. For the defect modes, the inverse participation ratio gradually increases, the effective mode width narrows, and the variability of the mode's center position increases. These changes indicate that the degree of localization of the defect modes gradually increases, potentially approaching Anderson localization. The defect modes undergo a second-stage localization transition, becoming more strongly localized. In addition, as the number of defect layers increases, the degree of localization strengthens, and the effective mode width continues to narrow. This study presents a unique system for investigating Anderson localization and is significant for the realization of low-threshold lasers.

Quantum transport plays a central role in both fundamental physics and the development of quantum technologies. While significant progress has been made in understanding transport phenomena in quantum systems, methods for optimizing transport properties remain limited, particularly in complex quantum networks. Building on recent advances in classical network optimization via the generalized Doob transform, we introduce a method that extends this approach to quantum networks. Our framework leverages a single diagonalization of the system generator to efficiently tailor both the Hamiltonian and dissipative contributions, optimizing transport observables such as currents and activities. We demonstrate the method's effectiveness through extensive numerical explorations, showing that optimal performance arises from nontrivial modifications to both coherent and incoherent dynamics. We also assess the robustness of the optimization under constraints that preserve specific physical features, such as fixed dissipative structures and input-output interactions. Finally, we discuss the connection between optimized transport and centrosymmetry, highlighting the relevance of this property for enhanced transport efficiency in quantum systems.

In this paper, extended-range percolation for neighborhoods of rectangular shape on a square lattice is investigated by means of Monte Carlo simulations. We choose a rectangle with an aspect ratio of 2 : 1, with the long side indicating its orientation. Three types of orientation are considered, namely horizontal (model I), horizontal or vertical randomly with equal probability (model II), and both horizontal and vertical simultaneously (thus in the shape of a cross) (model III). Simulations of both bond and site percolation are performed on the basis of an effective single-cluster growth algorithm, and precise percolation thresholds are found. The asymptotic and finite-size behaviors between the thresholds $p_c$ and the coordination number $z$ for each type are also discussed. For bond percolation, the asymptotic value $z{p}_c$ of all three situations tends to Bethe-lattice behavior $(z{p}_c\sim 1)$, and the finite-$z$ correction is found to be consistent with $z{p}_c\sim 1+a_1{z}^{-1/2}+a_2{z}^{-1}+a_3{z}^{-3/2}$ given by Deng et al. [J. Phys.: Conf. Ser. 1163, 012001, (2019)]. Regarding site percolation, for model I, data fitting gives the value of $z{p}_c\sim 4.3951\left(1\right)$ for large $z$, compared to $z{p}_c=2^d{\eta }_c\sim 4.3954$, where ${\eta }_c=1.09884280\left(9\right)$ [Phys. Rev. E 86, 061109 (2012)] is the continuum percolation threshold of aligned squares. For model II with site percolation, the nonlinear behavior of $z{p}_c$ versus $1/z$ shows that the orientation of the rectangle has an effect on the asymptotic behavior of $z{p}_c$. A variation of model II in which reciprocal neighborhoods are taken into account however shows linear behavior on such a plot. For model III, the fitting of the data leads to $z{p}_c\sim 4.414\left(2\right)$, which is in principle not related to the continuum threshold of overlapping crosses but close to the value $z{p}_c\approx 4.51235$ of overlapping disks. Some power laws of the simulation results are also discussed. The results show that the orientation of the rectangle has an impact on the thresholds of both bond percolation and site percolation, and a deeper analysis indicates that this effect gradually weakens as the coordination number $z$ increases, following a power law of $z^{-w}$ with $w=1.49\left(1\right)$ for bond percolation and 0.91(1) for site percolation for the difference between models I and II.

We study the fluctuation statistics of integrated currents in noisy quantum diffusive systems, focusing on the quantum symmetric simple exclusion and inclusion processes (QSSEPs and QSSIPs). These one-dimensional fermionic (QSSEP) and bosonic (QSSIP) models feature stochastic nearest-neighbor hopping driven by Brownian noise, together with boundary injection and removal processes. They provide solvable microscopic settings in which quantum coherence coexists with diffusion. Upon noise averaging, their dynamics reduce to those of the classical SSEP and SSIP. We show that the cumulant-generating function of the integrated current, at large scales, obeys a large deviation principle. To leading order in system size and for each noise realization, it converges to that of the corresponding classical process, establishing a classical typicality of current fluctuations in these noisy quantum systems. We further demonstrate a direct connection with macroscopic fluctuation theory (MFT), showing that the large-scale equations satisfied by biased quantum densities coincide with the steady-state Hamilton equations of MFT, thereby providing a microscopic quantum justification of the MFT framework in these models. Finally, we identify the leading finite-size corrections to the current statistics. We show the existence of subleading contributions of purely quantum origin, which are absent in the corresponding classical setting, and provide their explicit expressions for the second and third current cumulants. These quantum corrections are amenable to direct experimental or numerical verification, provided sufficient control over the noise realizations can be achieved. Their presence points toward the necessity of a quantum extension of MFT.

Linear response theory lies at the foundation of transport phenomena, predicting that physical systems respond proportionally to weak external forces. Here, we show that this principle can break down in a minimal nonequilibrium setting due to state-dependent stochastic resetting. We consider a Langevin particle driven by a constant external force $F$ and subject to a velocity-dependent resetting rate $r\left(v\right)={\lambda \left|v\right|}^{\alpha }$, where $\alpha$ controls the velocity dependence of the resetting. We derive the exact steady-state velocity distribution and establish a moment balance relation that links external driving, viscous dissipation, and resetting-induced dissipation. This relation reveals that the response is controlled by a nonlinear coupling between the velocity and the resetting rate, leading to nonlinear transport. In the deterministic limit without friction and diffusion, the mean velocity obeys the exact power law $\langle v\rangle \propto F^{1/(\alpha +1)}$ at all force strengths. In the presence of friction or velocity diffusion with $\alpha >0$, linear response is recovered at weak driving, followed by a crossover to the same nonlinear scaling at strong driving. Our results provide a solvable example in which linear response fails at the level of the leading-order behavior and identify velocity-dependent resetting as a minimal dynamical mechanism for generating nonlinear transport in nonequilibrium steady states. More broadly, they suggest a framework for understanding transport in stochastic systems with feedback or environment-dependent dynamics.

We investigate a three-dimensional Kuramoto model with nonlinear mean-field coupling, where the interaction strength depends on the macroscopic coherence through nonlinear feedback from the global order parameter. In the thermodynamic limit, a self-consistency analysis reveals multiple solution branches, including an additional branch between partially coherent and completely synchronized states, leading to bistability, controlled by the feedback parameters. This is a distinctive feature of the three-dimensional Kuramoto model with nonlinear mean-field coupling, which is absent in the classical three-dimensional Kuramoto model. Using the reduced dynamics based on the Ott-Antonsen ansatz and direct numerical simulation, we show that the system exhibits a two-step synchronization transition. While the transition from incoherence to partial coherence remains discontinuous at zero coupling for all parameter values, the transition from partial coherence to completely synchronized states can be continuous or discontinuous depending upon the feedback parameters. In the discontinuous regime, the coexistence of steady states leads to hysteresis. The observed hysteresis remains robust over the range of system sizes investigated. We further show that the hysteresis begins only above a threshold value of the feedback strength. These results demonstrate that nonlinear adaptation of the coupling provides a mechanism for controlling synchronization transitions and bistability in higher-dimensional systems.

Cell migration plays a fundamental role in numerous physiological processes, including embryonic development, wound healing, and cancer metastasis. While cell-cell adhesion is known to regulate motion by shaping cell morphology and intercellular force balance, its dynamic, rate-dependent contributions to tissue behavior remain poorly understood. In this study, we examine how the dissipative nature of cell-cell adhesion influences tissue dynamics and collective migration using an extended vertex model with explicit junctional viscosity. Our findings reveal a nontrivial interplay between two distinct components of adhesion: An interfacial adhesion energy (energetic, rate-independent) contribution, which sets the effective junctional tension, and a dissipative (rate-dependent) contribution, which controls resistance to relative motion during cell rearrangements. We show that increasing the energetic component promotes migration by modifying cell shape and lowering the barrier to neighbor exchanges, whereas strengthening the dissipative component induces jamming and suppresses cell motion. Linear rheological analysis further demonstrates that, in the unjammed regime, vertex-model tissues exhibit power-law viscoelastic behavior, with adhesion modulating the power-law exponent and thereby controlling the spread of relaxation timescales. Together, these findings clarify the dual role of adhesion in governing tissue mechanics and rheology and provide a mechanistic framework for understanding the balance between fluidity and rigidity in epithelial monolayers.

Nonthermal power-law spectra with index $-2$ are ubiquitously observed in turbulent wakefield acceleration, yet their statistical origin remains unresolved. Using one-dimensional particle-in-cell simulations with particle tracking, we analyze the stochastic energy evolution of electrons accelerated by turbulent wakefields and construct the transition probability density (TPD) of energy jumps. We show that the particle population separates into three dynamical regimes. Low-energy particles exhibit a superposition of Brownian diffusion and Lévy-type jump process, moderate-energy particles are dominated by Lorentzian-type TPDs indicating a nonlocal Lévy-type jump process in momentum space, and high-energy particles undergo ballistic acceleration. The Lorentzian-type TPD in the nonthermal regime naturally leads to a fractional Fokker-Planck description with fractional index $\alpha =1$, whose analytical solution yields a robust $f\left(\gamma \right)\propto {\gamma }^{-2}$ spectrum. Comparison with the $\kappa$ distribution confirms consistency with strongly nonthermal plasmas while revealing fractional transport as the dynamical origin of the universal index $-2$ heavy tail.

Mechanical desorption of a regular multiblock copolymer chain grafted at one end to an impenetrable, flat surface is studied theoretically. The polymer consists of alternating blocks of adsorption-active and nonactive monomer units. Two modes of desorption corresponding to two conjugate thermodynamic ensembles are considered and compared: isometric ensemble, where desorption is implemented by moving the chain free end from the surface to the distance $z$, and isotensional ensemble, where a constant pulling force $f$ is applied to the free chain end. Chain confirmations are modeled as simple random walks on a cubic lattice. It is shown that in the isometric ensemble reaction force versus distance dependence exhibits a characteristic sawtooth pattern due to the blocky structure of the copolymer, reflecting sequential detachment of adsorbing blocks followed by relaxation of nonadsorbing blocks. In the isotensional ensemble, desorption occurs as an abrupt “all-or-none” transition at some critical value of applied force; near the transition point, the probability distribution of the chain end position is multimodal. The results show that the shape of the detachment curve depends on the sequence structure, composition, and length of the blocks, as well as on the choice of the end through which the chain is grafted to the surface.

The melting transitions of a colloidal lattice confined to a two-dimensional $\left(2\text{D}\right)$ periodic substrate of square symmetry are studied using Monte Carlo simulations for the case when the number of colloidal particles per unit cell of the substrate is one. When the strengths of interparticle and particle-substrate interactions are comparable, the incommensurate nature of square and triangular ordering leads to the formation of a partially pinned solid with only one of the smallest G vectors of the substrate present. This low-temperature phase has true long-range order. By varying the lattice parameter of the substrate while keeping the number of colloidal particles per unit cell of the substrate constant, it is seen that the transition from this low-temperature solid to a high-temperature modulated liquid phase can happen via either a single crossover transition or by a two-stage melting process. Single crossover is observed when the substrate-particle interaction becomes dominant over the particle-particle interaction. This can happen either via an explicit increase in substrate strength or as the substrate lattice parameter increases. For the two-stage melting scenario, the intermediate phase is found to be hexatic. The transitions observed in this work differ in certain aspects from the predictions of the KTHNY theory. The study reveals how constraints from substrate periodicity can fundamentally alter melting dynamics, offering insights into the design of tunable colloidal systems and advancing the understanding of phase transitions in two-dimensional particle systems.

Inert polymer crowders ubiquitously promote the liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), yet the underlying mechanisms remain elusive. By evaluating the potential of mean force between polyampholyte-like IDPs, we demonstrate that the presence of inert polymer crowders induces conformational transitions by screening the excluded-volume interactions of the IDPs, indirectly enhancing interchain electrostatic correlations. Under physiological conditions, this enhanced correlation is sufficient to trigger LLPS of highly charged IDPs that would otherwise remain dispersed. Our work highlights a universal crowder-conformation-electrostatics coupling in driving LLPS.

Spectral statistics probe integrability versus chaos and have recently been extended to Markovian open quantum systems described by Lindbladians, whose quantum-trajectory unraveling decomposes the evolution into no-jump dynamics generated by an effective non-Hermitian Hamiltonian and recycling jumps. In this work, we perform spectrum-statistics diagnostics for Lindbladians and their effective non-Hermitian Hamiltonians. We show that recycling processes, symmetry constraints, and the Liouville-space structure crucially shape the spectral correlations. In particular, we identify a family of spectrally separable Lindbladians whose spectra exhibit robust Poisson statistics, despite the effective non-Hermitian Hamiltonian varying from Poisson to strongly correlated complex-spectrum statistics. Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians, deepening our understanding of spectral properties in open many-body systems.

We investigate a variant of coupled Kuramoto oscillators in which the effective coupling is modulated by the global coherence in a nonlinear fashion. In the thermodynamic limit, a self-consistency analysis reveals the manifestation of coexisting incoherent and coherent states in a finite range of the coupling strength, resulting in the bistability, the width of which is controlled by the feedback strength and the degree of the nonlinearity in the order parameter. For finite populations, intrinsic fluctuations fundamentally reshape this scenario: the synchronization transition manifests even at coupling strengths below the thermodynamic threshold. Strong feedback in combination with weak nonlinearity accelerates the onset of coherence at smaller coupling strengths, whereas strong feedback together with pronounced nonlinearity significantly enlarges the bistable region. Notably, this trend contrasts with the thermodynamic limit, where increasing nonlinearity suppresses the bistability. As the system size increases, the critical coupling strength approaches the thermodynamic-limiting value. Stronger nonlinear feedback facilitates the onset of the coherence closer to the thermodynamic critical coupling even for relatively smaller system sizes, thereby steering both the nature of the transition and its finite-size scaling. In addition, the theoretical estimates of the order parameter using the Ott-Antonsen ansatz and the finite-size scaling also corroborate the observed finite-size effects.