Power spectral densities are often interpreted through ensemble averages and long-time asymptotics. In many experiments, however, only a single finite record is available, so spectral estimators remain broadly distributed, and the usual independence assumptions across frequencies need not hold. Here we develop an exact finite-$T$ multispectral theory for an overdamped Brownian particle in a harmonic trap. For a collection of frequencies $\left\{{\omega }_i\right\}$, we obtain an exact characterization of the joint law of the finite-time estimators $\left\{S({\omega }_i,T)\right\}$, together with a covariance-explicit Gaussian representation for the associated Fourier projections. This representation makes the observation-window-induced interfrequency correlations explicit and shows how they vanish as $T\to \infty$, thereby recovering the asymptotic Whittle picture. We then use this structure to formulate a hierarchy of spectral likelihoods for inference from a single trajectory, ranging from the factorized Whittle approximation to blockwise covariance-aware approximations in frequency space. Monte Carlo simulations validate the finite-time theory and quantify the effect of neglected cross-frequency correlations on single-trajectory estimates of the trap parameters. Our results provide a controlled finite-time benchmark for spectral inference beyond the asymptotic regime.

We investigate the angular momentum and kinetic energy of a classical charged Brownian particle in a static magnetic field within the framework of the generalized Langevin equation with Ornstein–Uhlenbeck noise. The mean kinetic energy retains its equilibrium value for all times after the external field is switched on. An analytical expression for the mean time-dependent angular momentum is derived and supported by high-precision numerical calculations. We show that, in the long-time limit, the mean angular momentum approaches a finite nonzero value. While this result might appear to contradict the Bohr–van Leeuwen theorem, we demonstrate that the system considered here does not correspond to a canonical equilibrium ensemble due to the absence of spatial confinement. In particular, although the velocity distribution thermalizes, the position of the particle remains unbounded, and the partition function over position space is not normalizable. The obtained nonzero angular momentum should therefore be interpreted as a property of a nonequilibrium asymptotic dynamical regime within the Langevin description rather than as a violation of equilibrium statistical mechanics. The present results provide a transparent analytical reference for stochastic dynamics of charged particles in magnetic fields and highlight the role of unbounded motion and noncommuting limits in such systems.

We investigate non-Markovian stochastic processes with long-range temporal memory described by a generalized Langevin (Mori-Zwanzig) equation with a power-law memory kernel. Special attention is paid to the critical regime where the system parameters lie on the boundary separating stable and unstable dynamics, leading to diffusionlike behavior with memory. We derive analytical expressions for the asymptotic behavior of the process and show that, under appropriate conditions on the memory kernel, the system exhibits superdiffusive scaling. In particular, we establish an explicit relation between the exponent of the power-law memory kernel and the growth rate of the variance. Analytical predictions are supported by numerical simulations, confirming the emergence of superdiffusive regimes in systems with long-range memory.

We study two-banded, non-Hermitian random matrices inspired by sparse neural networks with a circular, one-dimensional topology. We focus on two paradigmatic models, a Su-Schrieffer-Heeger (SSH) chain and a ladder model, which have both non-Hermitian directional bias and random sign disorder in the hoppings. The random sign disorder, which follows Dale's law, leads to localization of the eigenstates, while the directional bias drives a delocalization transition in these states. The competition between disorder and directional bias results in rich eigenspectra with loops of extended states in the complex plane surrounded by regions of localized ones, and the eigenvalues are all confined to an annular region. Furthermore, the distinct band structures of the SSH chain and ladder model lead to different delocalization phenomena. Even in the absence of disorder, tuning the directional bias can lead to an eigenvalue degeneracy, which is an exceptional point for the SSH chain but a diabolic point for the ladder. In the presence of the disorder, these special eigenvalue degeneracies are preserved and also highlight key stages in the delocalization process. For both models, increasing the directional bias initially delocalizes states starting from within the bands. For the SSH chain, for large enough directional bias, the delocalized states open up a hole in the spectrum in the complex plane, similar to prior results for single band systems. But for the ladder model, as the directional bias is increased, the states delocalize in two stages, leading to two separate loops of extended states with localized states in between. The precise contours on which the extended states reside can be predicted from the Lyapunov exponents associated with products of random transfer matrices, in agreement with direct numerical diagonalization. Although we focus on periodic boundaries, results are discussed for open boundaries as well.

We study the response of Chua's circuit driven by a chaotic signal of variable timescale. We observe that when the frequency of the driving signal is significantly lower than that of the response and the driving strength is above a threshold, Chua's circuit exhibits multiple stable attractors. The features of the attractors change as the driving strength $\varepsilon$ increases; for instance, the attractors are double-scroll at low $\varepsilon$ and are single-scroll when $\varepsilon$ is high. We also investigate generalized synchronization (GS) between the drive and the response systems by employing the auxiliary system approach. When the drive is much slower than the response, we observe different scenarios of remote synchronization (RS) between response and auxiliary units. In addition to complete synchrony between response and auxiliary systems indicating GS between drive and response, we notice that the response and auxiliary units can be lag-synchronized and can also have correlated trajectories indicating novel forms of RS. The slow drive can induce multistability between these RS states, which disappears as the frequency of the driving signal increases and becomes equivalent to that of the response of Chua's circuit.

We investigate the coarsening kinetics in a long-range variant of the persistent voter model in space dimensions $d=1$ and 2. In this model, agents can hold two confidence levels, normal and zealot. Normal agents imitate another opinion chosen at a distance $r$ with probability $P\left(r\right)\propto r^{-\alpha }$, with $\alpha >d$. On the contrary, while in the zealot state, agents keep their own opinion. Normal (zealot) agents can become zealots (normal) if their opinion is equal (different) to that of the chosen neighbor. Through numerical simulations, we show that, for any values of $\alpha$, the model belongs to the same universality class as the long-range Ising model quenched to a small (nonzero) temperature, similarly to what was already known for the nearest-neighbor case. For the one-dimensional case, we further develop an analytical treatment, which reproduces the $\alpha$-dependence of the correlation length and the functional form of the correlation function. These results not only confirm that the introduction of opinion inertia mitigates the strong interfacial noise present in the voter model, thus reinstating the basic kinetic mechanism of the Ising model, but also expand the applicability of this correspondence.

We analyze a multi-phase-field model for an epithelial monolayer with pairwise adhesions between neighboring cells following an Ornstein-Uhlenbeck process, representing the stochastic turnover of junctional molecular motors. These fluctuations in junctional adhesion result in rearrangements in the tissue, fluidizing it and producing diffusive cell motion. Similar junctional fluctuations have proven a very useful tool in the vertex model literature, and we hope they will be equally helpful to the multi-phase-field model approach. Moreover, we observe that the cells' effective diffusion coefficient depends nonmonotonically on the persistence time of the fluctuations, confirming results previously observed in the vertex model.

Previous studies dealing with Floquet stability analysis of non-zero-mean time-modulated Rayleigh-Bénard convection have shown the existence of only harmonic and subharmonic instability modes. Here, we emphasize the existence of quasiperiodic instabilities that have not yet been reported in the literature. This is achieved through both a Floquet-based analysis of the basic state and direct numerical simulations of the linearized stability equations. Particular attention is devoted to highlighting the existence of kinks in the numerically computed marginal stability curves that render difficult the detection of the stability exchange between quasiperiodic instabilities and their harmonic and subharmonic counterparts. Depending on the Prandtl number of the working fluid, such instability exchanges set in via either bicritical states or the migration of complex-conjugate pairs Floquet multipliers which can be combined to produce subharmonic responses.

Wall roughness plays a central role in determining turbulent friction in pipe flows, yet most predictive frameworks continue to characterize the wall by a single effective roughness scale. Classical datasets—notably Nikuradse's sand-grain experiments and the rough-pipe measurements of Colebrook and White—demonstrate that this description is incomplete: surfaces with comparable nominal roughness heights can exhibit markedly different friction curves, including branch splitting and multiregime behavior. Reexamining the Colebrook-White experiments, we identify clear evidence of multiscale additivity, whereby the contribution of a smaller roughness scale enters once it becomes dynamically accessible and increases approximately linearly with its areal coverage. Motivated by this observation, we develop a multiscale extension of the Gioia-Chakraborty momentum-transfer framework in which roughness elements at distinct geometric scales contribute additive increments to the total friction. In the model, each scale becomes dynamically active when its height exceeds a Reynolds-number-dependent viscous cutoff proportional to the Kolmogorov length, while its contribution is weighted by a scale-dependent coefficient representing the geometric prominence of that roughness scale. This construction generalizes the original scale-selection mechanism by allowing multiple roughness scales to participate concurrently in outer-layer momentum transfer. The resulting framework provides a unified and continuous description connecting the classical roughness-dominated Nikuradse-Strickler regime, Colebrook-White-type trends at intermediate roughness, and smooth-wall behavior. For the applications considered here, however, the model coefficients are not uniquely determined from surface properties and are selected in a data-guided manner; establishing a quantitative mapping from measured surface topography to these coefficients remains an open problem.

When a horizontal plate vibrates strongly enough, it causes small particles such as sand grains to continually bounce on it and, over time, to diffuse across its surface. This phenomenon is the cause of the well-known Chladni figure, which is drawn by a higher density of grains gathering along the nodal lines of a resonating elastic plate. Using a heterogeneous, nonresonating plate, we investigate experimentally this type of diffusion. We find that, for the most part, it is comparable to classical molecular diffusion. We can define a temperature for the bouncing grains, and the system then obeys the fluctuation-dissipation theorem. We also recover Maxwell-Boltzmann statistics at equilibrium, when temperature is uniform. However, when temperature varies across the vibrating plate, the microscopic details of the grains' dynamics affect their macroscopic behavior: Fick's law, for instance, no longer applies. Instead, our experiments support a new transport relation that was recently proposed to represent diffusion in Chladni's experiment. Finally, we propose an expression for the heat flux associated to the nonequilibrium steady state predicted by this new relation and test it against observations.

Thermodynamic uncertainty relations (TURs) bound current precision by entropy production, but transport of noncommuting (non-Abelian) charges lacks a single joint classical record of all current components. We derive an operational, process-level matrix TUR for this setting from the entropy production $\mathrm{\Sigma }=D({\rho }_{SE}^{\prime }\parallel {\rho }_S^{\prime }\otimes {\rho }_E)$. Isolating the bath divergence $D_{\mathrm{bath}}=D({\rho }_E^{\prime }\parallel {\rho }_E)$, we prove a fully nonlinear, saturable lower bound valid for arbitrary current vectors $\mathrm{\Delta }q$: $D_{\mathrm{bath}}\ge B(\mathrm{\Delta }q,V,V^{\prime })$, where the bound depends only on the transported-charge signal $\mathrm{\Delta }q$ and on the pre- and postcollision covariance matrices $V$ and $V^{\prime }$ reconstructed from separate probe measurement settings. In the small-fluctuation regime $D_{\mathrm{bath}}\ge \frac{1}{2}\mathrm{\Delta }{q}^{\mathsf{T}}{V}^{-1}\mathrm{\Delta }q+{O(\parallel \mathrm{\Delta }q\parallel }^4)$, while beyond linear response the full integral bound remains valid. Numerical strong-coupling qubit collisions illustrate the bound and its near-saturation using only local measurements on the bath probe.

Processes controlled by stochastic synthesis and degradation (SSD) are widespread in biology but their reaction kinetics are not well understood. Using methods borrowed from the theory of resetting processes, we determine the first-passage properties of a collection of independent particles that are synthesized and degraded at constant rates, and follow an arbitrary diffusive motion. At equal synthesis and degradation rates, the mean reaction time with a target site can be minimized as in stochastic resetting, and a $CV$ criterion is derived. When the degradation rate is held fixed and the synthesis costs are taken into account, an optimal synthesis rate is obtained. In bounded domains, despite particle degradation, SSD improves the mean search time compared to a single nondegrading particle if the synthesis rate exceeds a critical value which obeys a universal relation. We illustrate these findings with Brownian diffusion on the infinite line and in an interval.

We study the equilibrium phase behavior of a fluid confined in a slit made from two patterned walls. Shearing the walls frustrates the fluid, due to a competition between capillary condensation and interface delocalization, forcing the formation of bridging phases with different pinning properties. This leads to an unusually rich phase diagram, displaying first-order and continuous phase transitions, depending sensitively on the slit width and shear. Generalized Kelvin equations determine the phase boundaries, while the bridging phases are characterized by large correlation lengths, predictions for which are tested using a microscopic density functional model.

We propose a model that extends the standard depinning paradigm by incorporating an aging mechanism into the local pinning force. This favors oscillations between a stuck state of large pinning and a slipping state of smaller pinning. We show that for mean field interactions between sites this mechanism can lead to the appearance of “king avalanches” and global instabilities, producing a global oscillatory stick-slip stress regime. We construct the phase diagram for this mean field case and identify regions of smooth dynamics, pure stick-slip, and bistability. Crucially, when considering two-dimensional systems with short-range interactions we find that states of global stress oscillation persist, but in contrast to the mean field case, no system-size avalanches appear. Instead, we observe alternating temporal intervals of larger and lower avalanche activity that correlate with the stress oscillations.

Statistical-gauge structures generated by current operators provide a symmetry-based description of forces and hyperforces in closed quantum statistical mechanics, but their status in open quantum dynamics remains largely unexplored. Here we develop a generalized statistical-gauge framework for Markovian open quantum systems governed by Lindblad evolution. The construction formulates statistical shifts in a smeared operator language, thereby avoiding singular local expressions while preserving the force and hyperforce content of the closed theory. Within this framework, the action of the Lindblad generator is analyzed in a jump-resolved representation that separates Hamiltonian transport from dissipative contributions in jump space. The central result is a modular Ward identity that holds for any full-rank quantum state, independently of equilibrium, stationarity, or unitary dynamics. We show that weak covariance is controlled by the full dissipative structure in jump space, rather than by invariance of individual jump operators or by particle-number conservation. This leads to a classification of continuum reservoirs according to density weight and spatial rate profile, and shows that Lindblad dynamics can deform the transported shift algebra through its product defect even when the bath is weakly covariant. Physically, the theory explains why uniform one-body loss or pumping may preserve the statistical-gauge structure, whereas density dephasing, multiparticle loss, and nonuniform bath profiles generically produce covariance-breaking residuals. These residuals provide practical diagnostics for reservoir engineering, approximate master equations, and numerical many-body simulations of open quantum systems.

Quantum chaotic systems exhibit certain universal statistical properties that closely resemble predictions from random matrix theory (RMT). With respect to observables, it has recently been conjectured that, when truncated to a sufficiently narrow energy window, their statistical properties can be described by a unitarily invariant ensemble, and testable criteria have been introduced, which are based on the scaling behavior of free cumulants. In this paper, we investigate the conjecture numerically in translationally invariant Heisenberg spin chains with spin quantum number $S=\frac{1}{2},1,\frac{3}{2}$. Combining a quantum-typicality-based numerical method with the exploitation of the system's symmetries, we study the spin current operator and find clear evidence of consistency with the proposed criteria in chaotic cases. Our findings further support the conjecture of the existence of RMT universality as manifest in the observable properties in quantum chaotic systems.

We analyze a continuous-time random walk model with stochastic reversals of direction. There is no external potential but the reorientation mechanism generates a nonzero current from asymmetry in the forward and backward waiting-time distributions (even when they have the same mean); the system can therefore be considered as a type of active particle ratchet. We derive an explicit expression for the mean ratchet current with exponentially distributed reorientation times and also develop a general renewal-theory framework to obtain the full large deviations, using this to comment on the possibility of dynamical phase transitions.

Extending the quantum formulation of Deffner and Jarzynski [Phys. Rev. X 3, 041003 (2013)] to a more general setting for studying the thermodynamics of information processing including initial correlations, we generalize the second law of thermodynamics to account for information processing in such autonomous systems. We consider a composite quantum system consisting of a principal system, heat bath, memory, and work source, and adopt an autonomous Hamiltonian framework. We present the following three main results. We first derive constraints on the total Hamiltonian that ensure the work source to act as a catalyst preserving its original randomness, given that the total unitary evolution must have a unitary partial transpose. Second, we generalize the quantum speed limit for the joint dynamics of system and memory to the quantum thermodynamic speed limit, from which we obtain a dynamical version of Landauer's bound. Finally, we also interpret this quantum thermodynamic speed limit in the context of quantum hypothesis testing.

We investigate phase separation dynamics in a binary mixture driven by a moving cooling source from which cold thermal fronts propagate radially into the surrounding mixture. The motion of the source introduces two distinct velocity scales: $v_s$ associated with the translation of the source and $v$ related to the propagation of the cooling thermal fronts. Using a modified Cahn-Hilliard-Cook model that explicitly couples the time-dependent temperature and concentration fields, we demonstrate that the competition between these two velocities fundamentally controls the morphology and kinetics of phase separation. Our numerical simulation results reveal a rich variety of nonequilibrium patterns whose characteristics depend not only on the ratio $v_s/v$ but also on the absolute values of $v_s$ and $v$. Same value of $v_s/v$ yields distinctly different patterns for different $v$. The spatial extent and shape of the quenched region, determined by the temperature profile delineating spatial regions with local temperatures above and below the demixing temperature dictates the domain morphology. Furthermore, unlike conventional isothermal phase separation, the system does not exhibit dynamical scaling of the equal-time two-point correlation function with a single growing length scale, reflecting the intrinsically nonstationary nature of phase separation driven by a moving quench source. Our results establish moving thermal sources as an effective means of controlling phase-separation pathways and provide a strategy for engineering desired pattern structures by tuning the two velocities.