We investigate a Brownian heat engine wherein a particle moves through a periodic ratchet potential under an exponentially decreasing temperature profile, a spatial configuration that closely resembles experimentally realizable conditions such as laser-induced thermal gradients and thermoplasmonic heating. This model yields exact analytical expressions for the particle current, thermodynamic efficiency, entropy production, and coefficient of performance (COP), and uniquely recovers the Curzon–Ahlborn efficiency and the corresponding endoreversible COP exactly in the quasistatic limit. These findings provide a rare and rigorous realization of endoreversible thermodynamics at the mesoscopic scale because they are derived directly from microscopic stochastic dynamics without recourse to phenomenological assumptions, asymptotic approximations, or coarse-graining techniques. Although the derived efficiency and COP are exact, they remain strictly below the Carnot limit, reflecting the inherent irreversibility embedded within the endoreversible framework. Furthermore, we show that in comparison to linear and piecewise-constant temperature profile cases, the exponential temperature profile leads to significantly higher particle velocities and higher entropy production, but lower thermodynamic efficiency, which underscores the fundamental trade-off between transport speed and energy cost. We further extend our analysis to networks of interacting Brownian motors operating in spatially nonuniform thermal environments. Numerical simulations confirm our analytical predictions and reveal the critical roles of temporal dynamics and external load in shaping motor performance, as well as transport directionality. Importantly, the exponential temperature profile is not only analytically tractable but also experimentally viable, providing a powerful platform for probing the emergence of macroscopic thermodynamic behavior from the underlying microscopic nonequilibrium dynamics.

We derive the characteristic function of stochastic functionals of a random walk whose position is reset to the origin at random times drawn from a general probability distribution. We analyze the long-time behavior and obtain the temporal scaling of the first two moments of any stochastic functional of the random walk when the resetting time distribution exhibits a power-law tail. When the resetting times probability density function has finite moments, the probability density of any functional converges to a delta function centered at its mean, indicating an ergodic phase. We explicitly examine the case of the half-occupation time and derive the ergodicity breaking parameter, the first two moments, and the limiting distribution when the resetting time distribution follows a power-law tail, for both Brownian and subdiffusive random walks. We characterize the three different shapes of the limiting distribution as a function of the exponent of the resetting distribution. Our theoretical findings are supported by Monte Carlo simulations, which show excellent agreement with the analytical results.

Devices based on nanonetworks have attracted growing interest due to their broad application potential. In this work, we investigate thermal transport in a quasirealistic nanonetwork model, where the nodes represent the cross junctions of atomic chains and the links consist of one-dimensional atomic chains. The results demonstrate that as the structural complexity of both weighted and unweighted networks increases, the thermal transport efficiency is significantly enhanced. To further elucidate the physical mechanism underlying this phenomenon, the effect of system complexity on phonon localization is examined through calculations of the phonon density of states and participation ratio. Based on these findings, we propose and validate an effective strategy for modulating thermal transport in nanonetworks by tuning the complexity of the network, offering new insights into the design of thermally functional materials and devices.

We study sums of independent and identically distributed random velocities in special relativity. We show that the resulting one-dimensional velocity distributions are not only stable under relativistic velocity addition, but define a genuinely new class of stochastic processes, namely relativistic Lévy processes. Given a system, this allows identifying distinct relativistic regimes in terms of the distribution's concavity at the origin and the probability of measuring relativistic velocities. These features provide a protocol to assess the relevance of stochastic relativistic effects in actual experiments. As supporting evidence, we find agreement with previous results about heavy-ion diffusion and show that our findings are consistent with the distribution of momentum deviations observed in measurements of antiproton cooling.

In this study, we explore an overdamped system of a dimer in a bistable potential immersed in a heat bath. The monomers interact via the combination of the Lennard-Jones potential and the harmonic potential. We have introduced a short-range interaction in our model making it more physical. Such a classical system can be used as a model for stochastic resonance (SR) based energy harvesters where the interplay between the noise, coupling, and a periodic perturbation leads to a rich class of dynamical behaviors. A key distinction between observing SR in single and coupled particle studies is that a transition between the two wells is only considered successful if both the particles cross a certain threshold position. Although we observe qualitatively a similar peaking behavior in different quantifiers of SR [like input energy ($W_p$) and hysteresis loop area], the effects of the above-mentioned condition on the dynamics of the system need to be further addressed. We study SR using different measures like the input energy per period of the external forcing, and the hysteresis loop area, as well as quantities like phase lag between the response and the external forcing and the maximum average amplitude of the response. Additionally, we have defined a quantity called the successful transition ratio. This ratio helps us understand the effects of the dimer's coupling on the number of successful transitions out of the total attempted transitions. The successful transition ratio is almost unity for a strongly coupled dimer suggesting most of the transition attempts end up successfully, however few they are in number. On the other hand, the ratio shows a peaking behavior with respect to noise for weak and intermediate couplings. We show that only for the weakly coupled dimer, the ratio is maximum around the temperature where SR takes place.

The interplay of quantum fluctuation through the Lee-Huang-Yang (LHY) correction and spin-orbit coupling can modify the stability of the ultradilute Bose-Bose mixtures and result in rich nonlinear physics. Here, under the action of spin-orbit coupling, LHY correction, and rotation, the ground state and vortex excitation of spin-orbit coupled Bose-Einstein condensates (BECs) with LHY correction trapped in a rotating potential are studied. Stable isotropic and anisotropic ground states with zero momentum (in the zero-momentum phase) and nonzero momentum (in the plane wave phase) are obtained. It is shown that anisotropic ground states are persistent near the phase boundary. Particularly, unpolarized and polarized vortex states are predicted. The phase transition condition, the effective mass and quadrupole surface mode describing the anisotropic (deformation) of the condensates, and the critical rotation frequency for vortex excitation are provided analytically. Owing to the action of spin-orbit coupling, the effective mass of the condensates is spatially dependent and asymmetric in two phases, resulting in distinct quadrupole modes, deformations, and vortex excitations in the two phases, especially when the LHY correction is present. The LHY correction promotes the system in the zero-momentum phase with unpolarized vortex states, while the spin-orbit coupling promotes the emergence of a plane wave phase with polarized vortex states. The phase transition and vortex excitation can be well manipulated by spin-orbit coupling, Raman coupling, LHY correction, and external potential.

We investigate the phenomenon of parametric instability in discrete models of spatiotemporally modulated materials. These materials are celebrated in part because they exhibit nonreciprocal transmission characteristics. However, parametric instability may occur for strong modulations, or occasionally even at very small modulation amplitudes, and prevent the safe operation of spatiotemporally modulated devices due to an exponential growth in the response amplitude. We use Floquet theory to conduct a detailed computational investigation of parametric instability. We explore the roles of modulation parameters (frequency, amplitude, wave number), the number of modulated units, and damping on the stability of the system. We highlight the pivotal role of spatial modulation in parametric instability, a feature that is predominantly overlooked in this context. We use the perturbation method to obtain analytical expressions for modulation frequencies at which the response becomes unstable. We hope that our findings enable and inspire new applications of spatiotemporally modulated materials that operate at higher amplitudes.

We investigate the universality in collisionless nonlinear dynamics of a codimension-two bifurcation where two eigenvalues collide at the origin, and two lines of continuous bifurcation and discontinuous jump meet. Through linear analysis and direct numerical simulations, we show that this bifurcation does occur, both for two-dimensional shear flows and for repulsive systems mimicking plasmas.

The bosonic magnetic ladder, a universal and the simplest model to reproduce the coupled effects of orbital magnetic field and optical lattices, provides an ideal platform for studying spin-orbit coupling, quantum phase transition and chiral topological states of matter. Here, considering both the on-site and rungwise interactions, the ground-state and chiral nonequilibrium dynamics of the bosonic magnetic ladder under an external harmonic trap are studied analytically and numerically. The threshold for the ground-state transition from the zero momentum state to the plane wave state is obtained. We find that the external harmonic potential has an important impact on the phase transition, which strongly depends on the magnetic field and an effective atomic interaction introduced by the interplay of on-site and rungwise interactions. The ground-state phase transitions can be well manipulated by changing the strengths of the external harmonic trap and rungwise interaction. Furthermore, by quenching the harmonic trap, rich nonlinear modes coupling and chiral nonequilibrium dynamics are revealed, which have distinct characteristics in different phases. Strong spin-momentum locking, softening of the collective modes and anharmonic collective dynamics are observed near the phase transition region. Particularly, novel nonlinear chiral dynamics induced by the interplay of strong spin-momentum locking and external trapping near the phase transition region are obtained, including the chiral out-of-phase oscillation of particles in the two legs (i.e., chiral opposite oscillation of particles in the two legs), chiral alternate oscillation of particles between the two legs (i.e., particles primarily populate the right (left) leg when moving away (returning to) the initial position), and chiral focusing-expanding transition of atomic wavepacket on the two legs (i.e., the wave packet exhibits a focused (expanded) state when moving toward (away from) the equilibrium point). Chiral dephasing and phase revival occur near the phase transition region, while coherent harmonic collective dynamics persists far away from the phase transition point. The observed chiralities can be well manipulated by the magnetic field.

We consider finite dynamical networks and define internal reliability based on the synchronization properties of a replicated unit or a set of units. If the states of the replicated units coincide with their prototypes, they are reliable; otherwise, if their states differ, they are antireliable. Quantification of reliability using the transversal Lyapunov exponent enables a straightforward analysis of different models. For a Kuramoto model of globally attractively coupled phase oscillators with a distribution of natural frequencies, we show that before the onset of synchronization peripheral frequency units (at the edges of the distribution) are antireliable, while central ones (with natural frequencies close to the mean frequency) are reliable. For repulsive coupling, the complementary configuration occurs, with central antireliable units and peripheral reliable ones. For this model, reliability can be expressed through phase correlations in a sort of fluctuation-dissipation relation. Sufficiently large subnetworks in the Kuramoto model are always antireliable; the same holds for a recurrent neural network, where individual units are always reliable. Furthermore, we show that other coupled oscillator models (Winfree-type coupled phase oscillators, coupled rotators, and coupled Stuart-Landau oscillators) demonstrate patterns of reliability and antireliability similar to those of the Kuramoto setup.

We investigate diffusion in a two-dimensional inverted soft Lorentz gas, where attractive Fermi-type potential wells are arranged in a triangular lattice. This configuration contrasts with earlier studies of soft Lorentz gases involving repulsive scatterers. By systematically varying the gap width and softness of the potential, we explore a rich landscape of diffusive behaviors. We present numerical simulations of the mean-squared displacement and compute diffusion coefficients, identifying tonguelike structures in parameter space associated with quasiballistic transport. Furthermore, we develop an extension to the Machta-Zwanzig approximation that incorporates correlated multihop trajectories, and we correct for the influence of localized periodic orbits. Our findings highlight the qualitative and quantitative differences between inverted and repulsive soft Lorentz gases, and they offer new insights into transport phenomena in smooth periodic potentials.

We experimentally investigated active particle-environment interactions in lemon billiards. To achieve this, we develop an Arduino robot to interact with the billiard table, which acts as our active particle, and control the shape of the lemon billiard with a parameter $\gamma \in [0,0.5]$. We experimentally confirm that the system's dynamics continuously change from regular $\gamma =0$ to fully chaotic $\gamma =0.5$, passing through cases of mixed-phase space for intermediate values of $\gamma$. We also analyze the robot's sensitivity to the initial conditions using the phase space as a function of time and the Lyapunov exponent to characterize the dynamics observed through the robot-environment interaction. Furthermore, we introduced a methodology based on recurrence analysis to compare numerical data with experimental data on a dynamical system. Numeric analyses complement the experimental results, showing a significant concordance. Our experimental setup presents an alternative method for measuring mixed-phase spaces in a billiard system outside the scope of optical physics. The robot-environment interaction provides an excellent alternative platform for experimental studies in physical systems, including additional aspects of chaos and dynamical systems, such as confined self-propelled particles and self-avoiding active particles.

We present a solution for the Green's function for the general case of a helical wormlike chain with twist-bend coupling and demonstrate the applicability of our solution for evaluating general structural and mechanical chain properties. We find that twist-bend coupling renormalizes the persistence length and the force-extension curves relative to wormlike chains. Analysis of intrinsically twisted polymers shows that incorporation of twist-bend coupling results in the oscillatory behavior in principal tangent correlations that are observed in some studies of synthetic polymers. The exact nature of our solution provides a framework to evaluate the role of twist-bend coupling on polymer properties, such as DNA bound to histones and motivates the reinterpretation of existing biopolymer experimental data.

Binary droplet collisions exhibit four primary outcomes at Weber number (We) below 100, i.e., bouncing, coalescence, reflexive separation, and stretching separation. At We exceeding 300, shattering becomes prominent, characterized by the catastrophic disintegration of the merged mass and ejection of satellite droplets. Previous numerical studies have largely focused on isolated regimes, with limited overlap across the full impact parameter space, and typically require regime-specific models. In this work, an integrated simulation approach is presented based on Smoothed Particle Hydrodynamics (SPH) to capture all major collision regimes from $\text{We}=10$ to 1000. This mesh-free method successfully reproduces both head-on and off-center collision outcomes for water, tetradecane, and heptane under near room conditions. The bouncing regime is modeled using an interfacial curvature-based approach tailored to account for hydrocarbon behavior, accurately replicating the transition to coalescence and stretching separation. The present SPH simulations capture the deformation morphologies and satellite droplet formation for stretching separation, while the critical We for reflexive separation is observed to be higher than experimental values. The shattering regime is validated for head-on collisions using the breakup diameter ratio, which shows strong agreement with experimental data in the range $\text{We}=200$–1500. This regime is further extended to off-center collisions, revealing subregimes. A comprehensive regime map is presented to illustrate the collision outcomes over the entire We range (0–1000).

The effect of the Ramsauer-Townsend effect, a quantum mechanical phenomenon, is investigated by generating an ultralow electron temperature plasma ($T_{\mathrm{e}}<1$ eV) in a weakly magnetized inductively coupled argon plasma using a dc-biased grid. In the ultralow electron energy regime, the Ramsauer-Townsend effect is maximized, significantly reducing electron-neutral collisions. Consequently, electron cyclotron resonance (ECR) heating remains effective even at high pressures $\left({\omega }_{\mathrm{c}}\ll \nu \right)$, where it is typically suppressed. The enhanced ECR heating leads to a remarkable increase in electron temperature from 0.43 to 1.1 eV. Furthermore, electrons exhibit nonlocal kinetics due to the Ramsauer-Townsend effect even under the condition where local electron kinetic behavior is generally expected. These results demonstrate that quantum scattering can sustain collisionlesslike ECR heating even in highly collisional plasmas, offering insights into plasma physics and transport, crucial for advanced quantum device fabrication.

Silicate melts play a crucial role in shaping Earth's geological features and influencing various geophysical phenomena. Transport properties of silicate melts control magma ocean dynamics on the early terrestrial planets and affect the chemical structure of Earth's deep interior. Here we have developed a deep-learning potential to investigate the structural evolution and transport properties of $\mathrm{CaSi}{\mathrm{O}}_3$ melt, a major component of basaltic magmas that is expected to exist in Earth's lower mantle. Our findings reveal that, with increasing compression, the average Si-O coordination number shows a nearly linear increase from fourfold at ambient pressure to sixfold in the lower mantle, with fivefold coordination serving as a transition state. The Ca-O coordination trend under compression parallels that of Si-O, except that sixfold coordination dominates at ambient pressure, while ninefold prevails at lower mantle pressure. At high pressures, the temporal evolution of cation-oxygen bonding exhibits frequent bond-breaking events. Meanwhile, the quantified lifetimes of different cation-oxygen species show that Ca species act as network modifiers, whereas Si species function as network formers. The calculated diffusion coefficients align favorably with available first-principles data, except in the supercooled state transition region. Between 2500 and 5000 K, viscosity increases with pressure, which can be attributed to enhanced structural polymerization due to the increased abundance of highly coordinated cation species. These insights into the $\mathrm{CaSi}{\mathrm{O}}_3$ melt could provide a fundamental basis for understanding the dynamics of magma ocean evolution.

This paper constitutes a step in the direction of developing integer lattice gas methods as an attractive alternative to lattice Boltzmann methods. Here we show that to Boltzmann limit the one-dimensional Blommel integer lattice gas is very close to entropic lattice Boltzmann. More interestingly, the integer lattice gas retains additional correlations that prevent the existence of a well-defined Boltzmann limit. In the analysis of the decaying sine wave we will see that in some situations the bulk viscosity can crucially depend on such correlations beyond the Boltzmann limit. A sampling collision operator, introduced here, can speed up the execution time to make the algorithm obtain comparable computational efficiency to entropic lattice Boltzmann methods.

Determining the local roughness exponent ${\alpha }_l$ in nonequilibrium surface growth is challenging when transient morphologies with long crossover times, such as those in Villain-Lai-Das Sarma (VLDS) models, obscure the asymptotic regime. It was only recently that numerical simulations of VLDS lattice models revealed that Optimal Detrended Fluctuation Analysis (ODFA) [Luis et al., Phys. Rev. E 95, 042801 (2017)] yields ${\alpha }_l$ values consistent with renormalization–group predictions for this class, even in transient regimes. However, a quantitative analytical framework explaining this agreement has been missing. Here, we close this gap by deriving how ODFA suppresses geometric corrections from local slope and curvature through the orthogonal projection of height fluctuations onto the local polynomial trend. We show that slope-induced corrections decay more slowly than curvature-induced ones, thereby dominating intermediate-scale biases. Our theoretical predictions are corroborated by numerical simulations of the Clarke-Vvedensky and Das Sarma-Tamborenea lattice models (with noise reduction), which confirm the predicted correction exponents in the small local-slope regime and the expected hierarchy in the suppression of slope and curvature effects.

We conjecture that the current fluctuations in one-dimensional driven transport systems obey an upper bound determined by the mean current and the driving force. This inequality originates from repulsive interactions between transporting particles, and the bound is approached both in near-equilibrium systems and in far-from-equilibrium systems with weak interactions. We first propose a coarse-grained model describing random particle exchanges between two reservoirs with constant rates, from which the upper bound emerges. We then rigorously prove the inequality in quantum ballistic transport systems. Finally, we demonstrate its validity in two specific diffusive systems: the exclusion process, for which the inequality can be proven, and charged-particle transport, for which numerical evidence supports the inequality.