We study integrability breaking and transport in a discrete space-time lattice with a local integrability-breaking perturbation. We find a singular distribution of the Lyapunov spectrum where the majority of Lyapunov exponents vanish in the thermodynamic limit. The subextensive sequence of nonzero exponents, converging in the thermodynamic limit, corresponds to Lyapunov vectors that are exponentially localized with localization lengths proportional to inverse Lyapunov exponents. Moreover, we investigate the transport behavior of the system by considering the spin-spin and current-current spatiotemporal correlation functions. Our results indicate that the overall transport behavior, similar to the purely integrable case, conforms to Kardar-Parisi-Zhang scaling in the thermodynamic limit and at vanishing magnetization. The same dynamical exponent $z=3/2$ governs the effect of local perturbation spreading in the bulk.

We investigate the interplay between parity-time-symmetry ($\mathcal{P}\mathcal{T}$-symmetry) breaking and localization transitions in non-Hermitian spin chains with an Aubry-André potential and competing Dzyaloshinskii-Moriya (DM) interactions. While prior studies (e.g., [S. Longhi, Phys. Rev. Lett. 122, 237601 (2019)]) suggest a universal alignment of $\mathcal{P}\mathcal{T}$ transitions and delocalization, our analysis of next-nearest-neighbor DM couplings reveals a critical deviation: the two phenomena decouple in certain parameter regimes, despite coinciding for nearest-neighbor interactions. Through eigenvalue analysis and inverse/normalized participation ratios (IPR/NPR), we identify three distinct phases: (i) extended states (weak potential), (ii) localized states (strong potential), and (iii) an intermediate hybrid phase unique to next-nearest-neighbor DM couplings. To unravel the dynamical fingerprints of these phases, we track the time-dependent density propagation, long-time survival probability, and phase-sensitive Loschmidt echo. The density evolution exhibits ballistic spreading in extended phases versus localized confinement, while the survival probability's decay rate, exponential in localized regimes versus algebraic in extended ones, serves as a clear phase discriminator. Notably, quenches between phases induce distinct dynamical signatures, with the Loschmidt echo sharply reflecting phase boundaries through its decay profile. These results establish dynamical metrics as indispensable tools for characterizing non-Hermitian phase transitions beyond spectral or localization measures.

We provide an exact formula for the mean first-passage time (MFPT) to a target at the origin for a single particle diffusing on a $d$-dimensional hypercubic lattice starting from a fixed initial position ${\vec{R}}_0$ and resetting to ${\vec{R}}_0$ with a rate $r$. Previously known results in the continuous space are recovered in the scaling limit $r\to 0, R_0=\left|{\vec{R}}_0\right|\to \infty$ with the product $\sqrt{r}{R}_0$ fixed. However, our formula is valid for any $r$ and any ${\vec{R}}_0$ that enables us to explore a much wider region of the parameter space that are inaccessible in the continuum limit. For example, we have shown that the MFPT, as a function of $r$ for fixed ${\vec{R}}_0$, diverges in the two opposite limits $r\to 0$ and $r\to \infty$ with a unique minimum in between, provided the starting point is not a nearest neighbor of the target. In this case, the MFPT diverges as a power law $\sim r^{\varphi }$ as $r\to \infty$, but very interestingly with an exponent $\varphi =\left(\right|m_1|+|m_2|+...+|m_d\left|\right)-1$ that depends on the starting point ${\vec{R}}_0=a(m_1,m_2,...,m_d)$ where $a$ is the lattice spacing and $m_i$'s are integers. If, on the other hand, the starting point happens to be a nearest neighbor of the target, then the MFPT decreases monotonically with increasing $r$, approaching a universal limiting value 1 as $r\to \infty$, indicating that the optimal resetting rate in this case is infinity. We provide a simple physical reason and a simple Markov-chain explanation behind this somewhat unexpected universal result. These interesting results on a lattice are not captured by the continuum theory. Our analytical predictions are verified in numerical simulations on lattices up to 50 dimensions. Finally, in the absence of a target, we also compute exactly the position distribution of the walker in the nonequlibrium stationary state that also displays interesting lattice effects not captured by the continuum theory.

The main question raised in the article is whether a neural network trained on a spin lattice model in one universality class can be used to test a model in another universality class. The quantities of interest are the critical phase transition temperature and the correlation length exponent. In other words, the question of transfer learning is how “universal” the trained network is and under what conditions. For this purpose, we applied a supervised learning procedure to three two-dimensional models for which critical properties are precisely known: The Ising model, the four-state Potts model, and the Baxter-Wu model. We consider two datasets: One with spin configurations and one with binding energy configurations. We find that estimates of the critical temperature agree well with the known results for both datasets, but not with the results of cross-testing using the energy datasets of the two models: The four-state Potts model and the Ising model. Estimates of the critical length exponent are less regular, and appear to be more accurate for energy datasets. A good example is the cross-testing using the energy dataset between the Ising model and the Baxter-Wu model in both training and testing directions.

We study the scaling behavior of chemical distances in spanning trees of critical site percolation clusters. Precisely, we analyze spanning trees constructed using four different algorithms: minimal path trees (MPTs), depth-first search (DFS), right-first search (RFS), and minimum spanning trees (MSTs). In each case, the chemical distance $\ell$ is not defined in the original percolation graph, but rather on the specific spanning tree generated by the chosen traversal rule. We analyze the conditional probability distribution $P_r\left(r\right|\ell )$, where $r$ is the Euclidean distance given a chemical distance $\ell$, and show that it follows a universal scaling form. Using scaling arguments and Bayes' theorem, we derive and numerically verify general relations between the characteristic exponents that govern these scaling laws. Each spanning-tree construction reveals the geometry of a different self-similar structure within the percolation cluster: MPTs yield the fractal dimension of the minimal path, MSTs recover the optimal path dimension, and DFS and RFS give the fractal dimension of the external hull in two dimensions. In three dimensions, the DFS tree reveals a previously unreported exponent, ${\theta }_1=1.575$, suggesting a new universality class for this type of self-similar structure. These results establish a general framework for extracting fractal dimensions of paths embedded in disordered media via spanning-tree-induced chemical distances.

We consider the boundary driven Quantum Symmetric Simple Inclusion Process (QSSIP) which describes a one-dimensional system of bosonic particles with stochastic nearest-neighbor hopping, modeled as a Brownian motion, with gain/loss processes at the endpoints of the chain driving the system out-of-equilibrium. Although the averaged QSSIP dynamics differs from that of the Quantum Symmetric Simple Exclusion Process (QSSEP)—the analogous system where bosons are replaced by fermions—we show that, paradoxically, the dynamics of their matrices of two-point functions, along with all their fluctuations, coincide. In contrary, the underlying classical models differs significantly, as the bosonic statistics allow the inclusion of multiple particles at the same site, in contrast to (symmetric) simple exclusion processes (SSEP). We provide an exact derivation of the large deviation function of density fluctuations in QSSIP and, as a consequence, in the classical inclusion process (SSIP) by exploiting its quantum formulation. Remarkably, our study highlights that, both in QSSEP and QSSIP, fluctuations of the local densities are typically classical, i.e., the cumulant generating functions of the local densities are asymptotically self-averaging and converge toward those of the classical SSEP and SSIP, realization-wise. This provides a test of the conjectured almost sure classical behavior of transport fluctuations, at leading order in the system size, in noisy diffusive quantum many-body systems.

We consider the thermalization hypothesis of pure states in nonintegrable quantum spin chains with conserved charges, including the nonintergable variants of the Ising chain with $Z_2$ symmetry, $XXZ$ chain with $\mathrm{U}\left(1\right)$ symmetry, and $XXX$ chain with $\mathrm{SU}\left(2\right)$ symmetries. Two kinds of pure states are considered: the energy eigenstates and the typical states evolved unitarily from the random product states for a long enough period. We further group the typical states by their expectation values of the conserved charges and consider the fine-grained thermalization hypothesis. We compare the locally (subsystem) reduced states of typical states/eigenstates with the ones of the corresponding thermal ensemble states. Besides the usual thermal ensembles such as the (micro)canonical ensemble without conserved charges and the generalized Gibbs ensemble (GGE) with all conserved charges included, we also consider the so-called partial-GGEs (p-GGEs), which include only part of the conserved charges in the thermal ensemble. Moreover, in the framework of p-GGE, the Hamiltonian and other conserved charges are on an equal footing. The introduction of p-GGEs extends quantum thermalization to a more general scope. The validity of the subsystem thermalization hypothesis can be quantified by the smallness of the relative entropy of the reduced states obtained from the GGE/p-GGE and the typical states/eigenstates. We examine the validity of the thermalization hypothesis by numerically studying the relative entropy demographics. We show that the thermalization hypothesis holds generically for small enough subsystems for various p-GGEs. Thus, our framework extends the universality of quantum thermalization.

We consider a generic class of stochastic particle-based models whose state at an instant in time is described by a set of continuous degrees of freedom (e.g., positions), and the length of this set changes stochastically in time due to birth-death processes. Using a master equation formalism, we write the dynamics of the corresponding (infinite) set of probability distributions: this takes the form of coupled Fokker-Planck equations with model-dependent source and sink terms. We derive the general expression of the entropy production rate for this class of models in terms of path irreversibility. To demonstrate the practical use of this framework, we analyze a biologically motivated model incorporating division, death, and diffusion, where spatial correlations arise through the division process. By systematically integrating out excess degrees of freedom, we obtain the marginal probability distribution, enabling exact calculations of key statistical properties such as average density and correlation functions. We validate our analytical results through numerical Brownian dynamics simulations, finding excellent agreement between theory and simulation. Our method thus provides a powerful tool for tackling previously unsolved problems in stochastic birth-death dynamics.

In the thermodynamic analysis of thermoelectric devices, typical irreversibilities are for the processes of finite-rate heat transfer, heat leak, and Joule heating. Approximate analyses often focus on either internal or external irreversibility, obtaining well-known expressions for the efficiency at maximum power (EMP), such as the Curzon-Ahlborn value for the endoreversible model and the Schmiedl-Seifert form for the exoreversible model. Within the Constant Properties model, we simultaneously incorporate internal as well as external irreversibilities. We employ the approximation of a symmetric and small external irreversibility, allowing a tractable expression for EMP that depends on three parameters: (1) the ratio of internal to external thermal conductance, (2) the figure of merit of the thermoelectric material, and (3) the ratio of hot and cold reservoir temperatures. We study limiting forms of this EMP and compare our framework with the exact model as well as with other irreversible models in finite-time thermodynamics, such as the minimally nonlinear model. In particular, we argue that the thermoelectric generator (TEG) in endoreversible approximation can be mapped to the mesoscopic model of Feynman's ratchet in the high-temperatures regime, thus providing an alternative to the viewpoint in literature where the ratchet in linear regime is mapped to an exoreversible TEG model. Finally, extending our study to the thermoelectric refrigerator under similar assumptions as for the generator, we analyze the efficiency at the maximum cooling power.

Following up on the recently published circuit theory for thermodynamic devices, we consider networks of thermoelectric converters (TECs) in stationary nonequilibrium. Assuming constant thermoelectric properties, the integration over a finite thickness of the linear local response of the thermoelectric material yields the nonlinear current-force characteristics. We show how to derive a choice of nonequilibrium conductance matrix summarizing the current-force characteristics for all available sets of currents and forces. This problem has infinitely many solutions if one considers only thermodynamic constraints. Each solution differs, among others, by the coupling between the currents. Then we determine the current-force characteristics of the serial (parallel) association of two TECs using the laws of resistance (conductance) matrix addition. For TECs in series, we find current-dependent boundary conditions for each subdevice. Since currents derive from composite potentials, we also associate the derivability and continuity of these potentials at the interfaces with conditions on thermoelectric coefficients. For TECs in parallel, we discuss the possibility of loop currents that are forbidden for the serial association.

We derive the nonequilibrium conductance matrix for open stationary chemical reaction networks (CRNs) described by a deterministic mass action kinetic equation. As an illustration, we determine the nonequilibrium conductance matrix of a CRN made of two pseudolinear subnetworks, called chemical modules, in two different ways: First by computing the nonequilibrium conductances of the modules that are then serially connected and second by computing the nonequilibrium conductance of the CRN directly. The two approaches coincide, as expected from our theory of thermodynamic circuits.

Out-of-time-ordered correlators (OTOCs) have emerged as powerful tools for diagnosing quantum chaos and information scrambling. While extensively studied in closed quantum systems, their behavior in dissipative environments remains less understood. In this work, we investigate the spectral decomposition of OTOCs in open quantum systems, using the dissipative modified kicked rotator as a paradigmatic model. By analyzing the eigenvalue spectrum of the quantum Liouvillian, we identify a crucial spectral truncation criterion that enables efficient modeling of OTOC dynamics. Our results reveal two distinct temporal regimes: a long-time decay phase governed by the spectral gap and an intermediate-time regime where a small subset of subdominant eigenvalues plays a crucial role. This spectral truncation criterion allows for efficient modeling of OTOC decay and reveals a direct connection between eigenvalue structure and information scrambling. Our results provide a quantitative framework for understanding OTOCs in dissipative quantum systems and suggest new avenues for experimental exploration in open quantum platforms.

Billiard models of single particles moving freely in two-dimensional regions enclosed by hard walls have long provided ideal toy models for the investigation of dynamical systems and chaos. Recently, billiards with (semi)permeable walls and internal holes have been used to study open systems. Here we introduce a billiard model containing an internal region with partial absorption. The absorption does not change the trajectories but instead reduces an intensity variable associated with each trajectory. The value of the intensity can be tracked as a function of the initial configuration and the number of reflections from the wall and depicted in intensity landscapes over the Poincaré phase space. This is similar in spirit to escape time diagrams that are often considered in dynamical systems with holes. We analyze the resulting intensity landscapes for three different geometries: a circular, elliptic, and oval billiard, respectively, all with a centrally placed circular absorbing region. The intensity landscapes feature increasingly more complex structures, organized around the sets of points in phase space that intersect the absorbing region in a given iteration, which we study in some detail. On top of these, the intensity landscapes are enriched by effects arising from multiple absorption events for a given trajectory.

Neural dynamics is determined by the transmission of discrete synaptic pulses (synaptic shot noise) among neurons. However, the neural responses are usually obtained within the diffusion approximation modeling synaptic inputs as continuous Gaussian noise. Here we present a rigorous mean-field theory that encompasses synaptic shot noise for sparse balanced inhibitory neural networks driven by an excitatory drive. Our theory predicts alternative dynamical regimes, in agreement with numerical simulations, which are not captured by the classical diffusion approximation. Notably, these regimes feature self-sustained global oscillations emerging at low connectivity (in-degree) via either continuous or hysteretic transitions and characterized by irregular neural activity, as expected for balanced dynamics. For sufficiently weak (strong) excitatory drive (inhibitory feedback) the transition line displays a peculiar reentrant shape revealing the existence of global oscillations at low and high in-degrees, separated by an asynchronous regime at intermediate levels of connectivity. The mechanisms leading to the emergence of these global oscillations are distinct: drift-driven at high connectivity and cluster activation at low connectivity. The frequency of these two kinds of global oscillations can be varied from slow ($\sim 1\mathrm{Hz}$) to fast ($\sim 100\mathrm{Hz}$) without altering their microscopic and macroscopic features by adjusting the excitatory drive and the synaptic inhibition strength in a prescribed way. Furthermore, the cluster-activated oscillations at low in-degrees could correspond to the $\gamma$ rhythms reported in mammalian cortex and hippocampus and attributed to ensembles of inhibitory neurons sharing few synaptic connections [Buzsáki and Wang, Annu. Rev. Neurosci. 35, 203 (2012)].

We study a system of globally coupled FitzHugh-Nagumo oscillators with pairwise and second-order interactions, showing that the presence of higher-order interactions substantially affects the character of the transition between synchronous and asynchronous states driven by changes in coupling strength. In particular, we demonstrate that, around the synchronization transition, solitary states emerge due to the presence of second-order interactions. We also show that, in contrast to the phenomenology observed in systems of phase oscillators, at low fixed pairwise coupling strengths, solitary states appear for both transition directions as the second-order interaction strength is varied, whereas for higher couplings they only occur in the forward direction, with the backward one characterized by explosive desynchronization.

We introduce a graph renormalization procedure based on the coarse-grained Laplacian, which generates reduced-complexity representations across scales. This method retains both dynamics and large-scale topological structures, while reducing redundant information, facilitating the analysis of large graphs by decreasing the number of vertices. Applied to graphs derived from electroencephalogram recordings of human brain activity, our approach reveals collective behavior emerging from neuronal interactions, such as coordinated neuronal activity. Additionally, it shows dynamic reorganization of brain activity across scales, with more generalized patterns during rest and more specialized and scale-invariant activity in the occipital lobe during attention.

The brain may adopt the strategy of lateral predictive coding (LPC) to construct optimal internal representations for salient features in input sensory signals, reducing the energetic cost of information transmission. Here we first consider the task of detecting one non-Gaussian signal by LPC from Gaussian background signals of the same magnitude, which is intractable by principal component decomposition. We study the emergence of the feature detection function from the perspective of tradeoff between energetic cost $E$ and information robustness, and implement this tradeoff by a thermodynamic free energy. We define $E$ as the mean $L_1$-norm of the internal state vectors, and quantify the level of information robustness by an entropy measure $S$. There are at least three types of optimal LPC matrices, one type with very weak synaptic weights and $S\approx 0$, and two functional types either with low energy $E$ or with high entropy $S$ in which one single unit selectively responds to the non-Gaussian input feature. The energy-information tradeoff induces two discontinuous phase transitions between these three types of optimal LPC networks. We then extend the discussion to detecting and distinguishing between two non-Gaussian input features and observe similar discontinuous phase transitions.

Fungi exhibit behaviors distinct from other microbes. Filamentous fungi grow by extending complex networks of branched filaments collectively referred to as the mycelium. These networks can expand over large distances and traverse low-nutrient areas by translocating nutrients through the filament network. This spatial characteristic makes filamentous fungi crucial for soil ecosystems, supporting stable microbial communities and promoting plant growth. However, simulating these behaviors is complex. The elongated nature of fungal compartments results in different mechanical interactions compared to the commonly modeled spherical bacteria. These detailed hyphal mechanics require specialized consideration and are often excluded from conventional fungal simulation packages. Additionally, the extensive fungal networks in nature demand computationally intensive simulations, necessitating high-performance algorithms. Therefore, realistic fungi simulations require specialized software. We introduce a fungal modeling expansion to the high-performance biological modelling and interface exchange (bmx) software suite. bmx leverages adaptive mesh refinement in AMReX for chemical diffusion and incorporates a full mechanical model for bacterial cells, accelerated by GPUs. By extending bmx to model filamentous particles, we demonstrate the formation of complex filament networks through interactions like hyphal branching and fusion (anastomosis). We show that the networks produced match real-world fungal structures through various metrics. This work supports computational studies of fungal growth dynamics and can be adapted to investigate the growth of other filamentous structures in biology or materials science. The expanded-BMX package is open-sourced and is available online.

The encapsulation of polyanions by virus coat proteins, whether single-stranded RNAs or synthetic polymers, is primarily driven by attractive electrostatic interactions between the positively charged, structurally disordered RNA binding domains of the virus coat proteins and the negatively charged polyanions. Theoretically, this interaction is often modeled by coarse-graining the charge distribution of the binding domains, either by projecting the charges onto the inner surface of the protein shell or by spreading them across a region representing the capsid lumen where the binding domains are located. In practice, however, the positive charges are not uniformly distributed across the binding domains, which themselves are positioned at discrete, specific sites on the shell surface. Here, we use molecular dynamics simulations to investigate the impact of localized interactions on the most probable or optimal length of the encapsulated polymer, revealing that the specific location of charges along the binding domains plays a significant role, consistent with experimental observations. Comparing the simulations with predictions from a simple mean-field theory taken from the literature, we find that while the general trends are reasonably well captured, quantitative discrepancies arise between the two approaches.