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We consider $30^{\circ}$ twisted bilayer formed by two copies of Haldane model and explore evolution of its properties with varying interlayer coupling strength. Specifically, we compute the system's energy spectrum, its fractal dimensions, topological entanglement entropy, local Chern markers and anomalous Hall conductivity. We find that at weak interlayer coupling, the system remains gapped and retains topological properties of the isolated layers, but at strong interlayer coupling, the system forms a gapless multifractal state. We also establish that anomalous Hall conductivity can be used to characterize the system's topological properties in the same way as a local Chern marker., Comment: 10 pages, 9 figures

We derive the expression for the entropy production for stochastic dynamics defined on a continuous space of states containing unidirectional transitions. The expression is derived by taking the continuous limit of a stochastic dynamics on a discrete space of states and is based on an expression for the entropy production appropriate for unidirectional transition. Our results shows that the entropy flux is the negative of the divergence of the vector firld whose components are the rates at which a dynamic variable changes in time. For a Hamiltonian dynamical system, it follows from this result that the entropy flux vanish identically.

Recently, a framework for computing the symmetry-resolved entanglement entropy for non-invertible symmetries in $1{+}1$d conformal field theories has been proposed by Saura-Bastida, Das, Sierra and Molina-Vilaplana [Phys. Rev. D109, 105026]. We revisit their theoretical setup, paying particular attention to possible contributions from the conformal boundary conditions imposed at the entangling surface -- a potential subtlety that was not addressed in the original proposal. We find that the presence of boundaries modifies the construction of projectors onto irreducible sectors, compared to what can be expected from a pure bulk approach. This is a direct consequence of the fusion algebra of non-invertible symmetries being different in the presence or absence of boundaries on which defects can end. We apply our formalism to the case of the Fibonacci category symmetry in the three-state Potts and tricritical Ising model and the Rep($S_3$) fusion category symmetry in the $SU(2)_4$ Wess-Zumino-Witten conformal field theory. We numerically corroborate our findings by simulating critical anyonic chains with these symmetries as a finite lattice substitute for the expected entanglement Hamiltonian. Our predictions for the symmetry-resolved entanglement for non-invertible symmetries seem to disagree with the recent work by Saura-Bastida et al., Comment: 32 pages, 14 figures

We study the roughening of interfaces in phase-separated active suspensions on substrates. At large length and timescales, we show that the interfacial dynamics belongs to the |q|KPZ universality class discussed in Besse et al. Phys. Rev. Lett. 130, 187102 (2023). This holds despite the presence of long-ranged fluid flows. At early times, instead, the roughening exponents are the same as those in the presence of a momentum-conserving fluid. Surprisingly, when the effect of substrate friction can be ignored, the interface becomes random beyond a de Gennes-Taupin lengthscale which depends on the interfacial tension.

Quantum states undergoing quantum chaotic dynamics are expected to evolve into featureless states at late times. While this expectation holds true on an average, coarse-grained level, it is unclear if this expectation applies to higher statistical moments, as symmetries typically present in physical systems constrain the exploration of phase space. Here we study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We identify two limiting universal regimes depending on the initial condition. When the initial state is typical -- all the moments of the symmetry operators are equal to those of pure random states -- then the late-time ensemble is indistinguishable from the Haar ensemble in the thermodynamic limit and at the level of higher statistical moments. Otherwise, atypical initial states evolve into non-universal ensembles which can be distinguished from the Haar ensemble from simple measurements or subsystem properties. Interestingly, such atypical initial conditions are not rare, even when considering product state initial conditions, and can be found in the middle of the spectrum of Hamiltonians known to be `maximally' chaotic. In the limiting case of initial states with negligible variance of the symmetry operator (e.g., states with fixed particle number or states with negligible energy variance), the late-time ensemble has universal behavior captured by constrained RMT ensembles. Our work shows that even though midspectrum states do not explore ergodically all of phase space at late times, the late-time ensemble typically -- but not always -- exhibits the same average and sample-to-sample fluctuations as the Haar ensemble., Comment: 14 pages, 5 figures

The spin-1/2 Heisenberg antiferromagnet on the diamond-decorated square lattice in the presence of a magnetic field displays various quantum phases including the Lieb-Mattis ferrimagnetic, dimer-tetramer, monomer-dimer, and spin-canted phases, in addition to the trivial fully saturated state. Thermodynamic properties of this model are investigated using several complementary analytical and numerical methods such as exact diagonalization up to the systems of 40 spins, an effective monomer-dimer description, sign-problem-free quantum Monte Carlo simulations for up to 180 spins, and a decoupling approximation. Our particular attention is focused on the parameter region favoring the dimer-tetramer phase. This ground state can be represented by a classical hard-dimer model on the square lattice and retains a macroscopic degeneracy even under a magnetic field. However, the description of the low-temperature thermodynamics close to the boundary between the macroscopically degenerate dimer-tetramer and the non-degenerate monomer-dimer phases requires an extended classical monomer-dimer lattice-gas model. Anomalous thermodynamic properties emerging in the vicinity of the dimer-tetramer phase are studied in detail. Under the adiabatic demagnetization we detect an enhanced magnetocaloric effect promoting an efficient cooling to absolute zero temperature, provided that the system reaches the dimer-tetramer ground state at zero field., Comment: 18 pages, 14 figures

Random magnetic field configurations are ubiquitous in nature. Such fields lead to a variety of dynamical phenomena, including localization and glassy physics in some condensed matter systems and novel transport processes in astrophysical systems. Here we consider the physics of a charged quantum particle moving in a ``magnetic maze'': a high-dimensional space filled with a randomly chosen vector potential and a corresponding magnetic field. We derive a path integral description of the model by introducing appropriate collective variables and integrating out the random vector potential, and we solve for the dynamics in the limit of large dimensionality. We derive and analyze the equations of motion for Euclidean and real-time dynamics, and we calculate out-of-time-order correlators. We show that a special choice of vector potential correlations gives rise, in the low temperature limit, to a novel scale-invariant quantum theory with a tunable dynamical exponent. Moreover, we show that the theory is chaotic with a tunable chaos exponent which approaches the chaos bound at low temperature and strong coupling.

Quantum circuits offer a versatile platform for simulating digital quantum dynamics and uncovering novel states of non-equilibrium quantum matter. One principal example are measurement-induced phase transitions arising from non-unitary dynamics in monitored circuits, which employ mid-circuit measurements as an essential building block next to standard unitary gates. Although a comprehensive understanding of dynamics in generic circuits is still evolving, we contend that monitored quantum circuits yield robust phases of dynamic matter, which -- akin to Hamiltonian ground state phases -- can be categorized based on symmetries and spatial dimensionality. To illustrate this concept, we focus on quantum circuits within symmetry classes BDI and D, which are measurement-only adaptations of the paradigmatic Kitaev and Yao-Kivelson models, embodying particle-hole-symmetric Majorana fermions with or without time-reversal. We establish a general framework -- Majorana loop models -- for both symmetry classes to provide access to the phenomenology of the entanglement dynamics in these circuits, displaying both an area-law phase of localized Majorana loops and a delocalized, highly entangled Majorana liquid phase. The two phases are separated by a continuous transition displaying quantum Lifshitz scaling, albeit with critical exponents of two distinct universality classes. The loop model framework provides not only analytical understanding of these universality classes in terms of non-linear sigma models, but also allows for highly efficient numerical techniques capable of simulating excessively large circuits with up to $10^8$ qubits. We utilize this framework to accurately determine universal probes that distinguish both the entangled phases and the critical points of the two symmetry classes. Our work thereby further solidifies the concept of emergent circuit phases and their phase transitions.

We study the ground-state phase diagram of an unfrustrated antiferromagnetic Ising chain with longitudinal and transverse fields in the full range of interactions: from all-to-all to nearest-neighbors. First, we solve the model analytically in the strong long-range regime, confirming in the process that a mean-field treatment is exact for this model. We compute the order parameter and the correlations and show that the model exhibits a tricritical point where the phase transition changes from first to second order. This is in contrast with the nearest-neighbor limit where the phase transition is known to be second order. To understand how the order of the phase transition changes from one limit to the other, we tackle the analytically-intractable interaction ranges numerically, using a variational quantum Monte Carlo method with a neural-network-based ansatz, the visual transformer. We show how the first-order phase transition shrinks with decreasing interaction range and establish approximate boundaries in the interaction range for which the first-order phase transition is present. Finally, we establish that the key ingredient to stabilize a first-order phase transition and a tricritical point is the presence of ferromagnetic interactions between spins of the same sublattice on top of antiferromagnetic interactions between spins of different sublattices. Tunable-range unfrustrated antiferromagnetic interactions are just one way to implement such staggered interactions., Comment: 14 pages, 9 figures

A comprehensive symmetry resolution of the entanglement entropy (EE) in $(1+1)$-d rational conformal field theories (RCFT) with categorical non-invertible symmetries is presented. This amounts to symmetry resolving the entanglement with respect to the generalized twisted and anyonic charge sectors of the theory. The anyonic sectors label the irreducible representations of a modular fusion category defining the symmetry and can be understood through the $(2+1)$-d symmetry topological field theory (SymTFT) that encodes the symmetry features of the CFT. Using this, we define the corresponding generalized boundary dependent charged moments necessary for the symmetry resolution of the entanglement entropy, which is the main result of this work. Furthermore, contrary to the case of invertible symmetries, we observe the breakdown of entanglement equipartition between different charged sectors at the next-to-leading order in the ultraviolet cutoff., Comment: 6 pages + 5 pages appendices, 1 figure

An understanding of the disease spreading phenomenon based on a mathematical model is extremely needed for the implication of the correct policy measures to contain the disease propagation. Here, we report a new model namely the Ising-SIR model describing contagious disease spreading phenomena including both airborne and direct contact disease transformations. In the airborne case, a susceptible agent can catch the disease either from the environment or its infected neighbors whereas in the second case, the agent can be infected only through close contact with its infected neighbors. We have performed Monte Carlo simulations on a square lattice using periodic boundary conditions to investigate the dynamics of disease spread. The simulations demonstrate that the mechanism of disease spreading plays a significant role in the growth dynamics and leads to different growth exponent. In the direct contact disease spreading mechanism, the growth exponent is nearly equal to two for some model parameters which agrees with earlier empirical observations. In addition, the model predicts various types of spatiotemporal patterns that can be observed in nature.

We study bipartite quantum systems kept at different temperatures where a tunnel coupling between the two subsystems induces transitions. We find two independent constraints on the temperature-bias-dependent, out-of-equilibrium tunneling rates between the two subsystems, which both turn out to be particularly restrictive when the coupled quantum systems are small. These bounds take the form of a thermodynamic and of an energetic constraint, as they are associated with the dissipated heat and with the absorbed energy required to establish and deplete the temperature bias, respectively. The derived constraints apply to a large class of experimentally accessible quantum systems: except for the restriction to the tunneling regime, they hold for arbitrary subsystem Hamiltonians, including interactions or non-linear energy spectra. These results hold for a large class of experimentally relevant systems, ranging from molecular junctions to coupled cavities, and can be tested by, for instance, measuring the out-of-equilibrium tunneling current and its noise.

Thermal transport is a fundamental mechanism of energy transfer process quite distinct from wave propagation phenomena. It can be manipulated well beyond the possibilities offered by natural materials with a new generation of artificial metamaterials: thermal metamaterials. Topological physics, a focal point in contemporary condensed matter physics, is closely intertwined with thermal metamaterials in recent years. Inspired by topological photonics and topological acoustics in wave metamaterials, a new research field emerged recently, which we dub `topological thermotics', which encompasses three primary branches: topological thermal conduction, convection, and radiation. For topological thermal conduction, we discuss recent advances in both 1D and higher-dimensional thermal topological phases. For topological thermal convection, we discuss the implementation of thermal exceptional points with their unique properties and non-Hermitian thermal topological states. Finally, we review the most recent demonstration of topological effects in the near-field and far-field radiation. Anticipating future developments, we conclude by discussing potential directions of topological thermotics, including the expansion into other diffusion processes such as particle dynamics and plasma physics, and the integration with machine learning techniques., Comment: This perpective summarizes the topological physics in thermal metamaterials and proposes a new research field, "topological thermotics"

The formation, dissolution, and dynamics of multi-particle complexes is of fundamental interest in the study of stochastic chemical systems. In 1976, Masao Doi introduced a Fock space formalism for modeling classical particles. Doi's formalism, however, does not support the assembly of multiple particles into complexes. Starting in the 2000's, multiple groups developed rule-based methods for computationally simulating biochemical systems involving large macromolecular complexes. However, these methods are based on graph-rewriting rules and/or process algebras that are mathematically disconnected from the statistical physics methods generally used to analyze equilibrium and nonequilibrium systems. Here we bridge these two approaches by introducing an operator algebra for the rule-based modeling of multi-particle complexes. Our formalism is based on a Fock space that supports not only the creation and annihilation of classical particles, but also the assembly of multiple particles into complexes, as well as the disassembly of complexes into their components. Rules are specified by algebraic operators that act on particles through a manifestation of Wick's theorem. We further describe diagrammatic methods that facilitate rule specification and analytic calculations. We demonstrate our formalism on systems in and out of thermal equilibrium, and for nonequilibrium systems we present a stochastic simulation algorithm based on our formalism. The results provide a unified approach to the mathematical and computational study of stochastic chemical systems in which multi-particle complexes play an important role., Comment: 26 pages, 9 figures

Analytic continuation (AC) from imaginary-time Green's function to spectral function is essential in the numerical analysis of dynamical properties in quantum many-body systems. However, this process faces a fundamental challenge: it is an ill-posed problem, leading to unstable spectra against the noise in the Green's function. This instability is further complicated in multi-orbital systems with hybridization between spin-orbitals, where off-diagonal Green's functions yield a spectral matrix with off-diagonal elements, necessitating the matrix's semi-positive definiteness to satisfy the causality. We propose an advanced AC method using sparse modeling for multi-orbital systems, which reduces the effect of noise and ensures the matrix's semi-positive definiteness. We demonstrate the effectiveness of this approach by contrasting it with the conventional sparse modeling method, focusing on handling Green's functions with off-diagonal elements, thereby demonstrating our proposed method's enhanced stability and precision., Comment: 8 pages, 8 figures

The critical phase boundary of a system, in general, can depend on one or more parameters. We show that by calculating the Gini index ($g$) of any suitably defined response function of a system, the critical phase boundary can always be reduced to that of a single parameter, starting from $g=0$ and terminating at $g=g_f$, where $g_f$ is a universal number for a given universality class. We demonstrate the construction with analytical and numerical calculations of mean field transverse field Ising model and site diluted Ising model on the Bethe lattice, respectively. Both models have two parameter phase boundaries -- transverse field and Temperature for the first case and site dilution and temperature in the second case. Both can be reduced to single parameter transition points in terms of the Gini index. The method is generally applicable for any multi-parameter critical transition., Comment: 5 pages, 4 figures

Using exact enumeration, the Casimir amplitude and the Casimir force are calculated for the square lattice Ising model with quenched surface disorder on one surface in cylinder geometry at criticality. The system shape is characterized by the aspect ratio $\rho=L/M$, where the cylinder length $L$ can take arbitrary values, while the circumference $M$ is varied from $M=4$ to $M=54$, resulting in up to $2^{54}$ numerically exact free energy calculations. A careful $M\to\infty$ extrapolation shows that quenched surface disorder is irrelevant in two dimensions, but gives rise to logarithmic corrections., Comment: 18 pages, 4 figures

Recently, the full version of the Eigenstate Thermalization Hypothesis (ETH) has been systematized using Free Probability. In this paper, we present a detailed discussion of the Free Cumulants approach to many-body dynamics within the microcanonical ensemble. Differences between the later and canonical averages are known to manifest in the time-dependent fluctuations of extensive operators. Thus, the microcanonical ensemble is essential to extend the application of Free Probability to the broad class of extensive observables. We numerically demonstrate the validity of our approach in a non-integrable spin chain Hamiltonian for extensive observables at finite energy density. Our results confirm the full ETH properties, specifically the suppression of crossing contributions and the factorization of non-crossing ones, thus demonstrating that the microcanonical free cumulants encode ETH smooth correlations for both local and extensive observables., Comment: 14 pages, 10 figures, accompanying paper to Arxiv:2303.00713

We compute the joint large deviation rate functional in the limit of large time for the current flowing through the edges of a finite graph for a boundary-driven zero-range dynamics. This generalizes one-dimensional results previously obtained with different approaches \cite{BDGJL1,HRS}; our alternative techniques illuminate various connections and complementary perspectives. In particular, we here use a variational approach to derive the rate functional by contraction from a level 2.5 large deviation rate functional. We perform an exact minimization and finally obtain the rate functional as a variational problem involving a superposition of cost functions for each edge. The contributions from different edges are not independent since they are related by the values of a potential function on the nodes of the graph. The rate functional on the graph is a microscopic version of the continuous rate functional predicted by the macroscopic fluctuation theory \cite{MFT}, and we indeed show a convergence in the scaling limit. If we split the graph into two connected regions by a cutset and are interested just in the current flowing through the cutset, we find that the result is the same as that of an effective system composed of only one effective edge (as happens at macroscopic level and is expected also for other models \cite{Cap}). The characteristics of this effective edge are related to the ``capacities'' of the graph and can be obtained by a reduction using elementary transformations as in electrical networks; specifically, we treat components in parallel, in series, and in $N$-star configurations (reduced to effective complete $N$-graphs). Our reduction procedure is directly related to the reduction to the trace process \cite{L} and, since the dynamics is in general not reversible, it is also closely connected to the theory of non-reversible electrical networks in \cite{B}., Comment: 35 pages, 6 figures

Rare events play a crucial role in understanding complex systems. Characterizing and analyzing them in scale-invariant situations is challenging due to strong correlations. In this work, we focus on characterizing the tails of probability distribution functions (PDFs) for these systems. Using a variety of methods, perturbation theory, functional renormalization group, hierarchical models, large $n$ limit, and Monte Carlo simulations, we investigate universal rare events of critical $O(n)$ systems. Additionally, we explore the crossover from universal to nonuniversal behavior in PDF tails, extending Cram\'er's series to strongly correlated variables. Our findings highlight the universal and nonuniversal aspects of rare event statistics and challenge existing assumptions about power-law corrections to the leading stretched exponential decay in these tails., Comment: 17 pages, 8 figures

Heisenberg model spin systems offer favorable and manageable physical settings for generating and manipulating entangled quantum states. In this work mixed spin-(1/2,1/2,1) Heisenberg spin trimer with two different but isotropic Lande g-factors and two different exchange constants is considered. The study undertakes the task of finding the optimal parameters to create entangled states and control them by external magnetic field. The primary objective of this work is to examine the tripartite entanglement of a system and the dependence of the tripartite entanglement on various system parameters. Particularly, the effects of non-conserving magnetization are in the focus of our research. The source of non-commutativity between the magnetic moment operator and the Hamiltonian is the non-uniformity of g-factors. To quantify the tripartite entanglement, an entanglement measure called "tripartite negativity" has been used in this work., Comment: 8 pages, 3 figures

The Maxwell stress tensor for the linear and uniform media in static electromagnetic field implies a new form of pressure caused by the mutual field energy density. When it is introduced into the fundamental thermodynamic equation for the media, we have a new pressure-volume work term. The combination of new term and proper electromagnetic work term naturally gives the well-known form that is currently obtained by a working hypothesis., Comment: 4 pages, 1 figure

We study the conformation and topological properties of cyclical star polymers with $f$ ring arms, each made of $n$ beads. We find that the conformational properties of unlinked cyclical star polymers are compatible to those of linear star polymers with $2f$ arms made of $n/2$ beads each. This compatibility vanishes when the topology of the star, measured as the degree of linking between arms, changes. In fact, when links are allowed we notice that the gyration radius decreases as a function of the absolute linking number $\vert Lk \vert$ of the arms, regardless of the protocol that is employed to introduce said links. Furthermore, the internal structure of the macromolecules, as highlighted by the radial density function, changes qualitatively for large values of $\vert Lk \vert$., Comment: 11 pages, 11 figures

We investigate, in an analytical fashion, quantum Carnot cycles of a microscopic heat engine coupled to two nite heat reservoirs, whose internal cycles could own higher e ciency than the standard Carnot limit without consuming extra quantum resources, e.g., coherence or squeezing properties. The engine runs time-dependently, involving both the internal and external cycles to collaboratively accomplish a complete Carnot cycle, and the e ciency of the engine depends on the reservoirs heat capacities and the working substance. Our analytical results of the maximum efficiency and the maximum power output clarify the mechanism behind the high performance of the microscopic engines, displaying the key roles played by the nite-sized heat reservoirs. Our proposal is generally valid for any microscopic thermodynamic system and fully feasible under current laboratory conditions.

The physical significance of the stochastic processes associated to the generalized Gibbs ensembles is scrutinized here with special attention to the thermodynamic fluctuations of small systems. The contact with the environment produces an interaction entropy, which controls the distribution of fluctuations and allows writing the generalized Gibbs ensembles for macrostates in potential form. This naturally yields exact nonlinear thermodynamic Langevin equations (TLEs) for such variables, with drift expressed in terms of entropic forces. The analysis of the canonical ensemble for an ideal monoatomic gas and the related TLEs show that introducing currents leads to nonequilibrium heat transfer conditions with interesting bounds on entropy production but with no obvious thermodynamic limit. For a colloidal particle under constant force, the TLEs for macroscopic variables are different from those for the microscopic position, typically used in the so-called stochastic thermodynamics; while TLEs are consistent with the fundamental equation obtained from the Hamiltonian, stochastic thermodynamics requires isothermal conditions and entropy proportional to position.

We present a comparative analysis of the plethora of nonextensive and/or nonadditive entropies which go beyond the standard Boltzmann-Gibbs formulation. After defining the basic notions of additivity, extensivity, and composability we discuss the properties of these entropies and their mutual relations, if they exist. The results are presented in two informative tables supposedly of strong interest to gravity and cosmology community in the context of explored vastly recent days the horizon entropies for black hole and cosmological models. This is since gravitational systems admit long-range interactions which usually lead to a break of the standard additivity rule for thermodynamical systems composed of subsystems in Boltzmann-Gibbs thermodynamics. The features of additivity, extensivity, and the composability are listed systematically. Some brief discussion on the validity of the notion of equilibrium temperature for nonextensive systems is also presented., Comment: 18 pages, 2 tables, prepared to the "Entropy" journal, comments are welcome

We study percolation problems of overlapping objects where the underlying geometry is such that in D-dimensions, a subset of the directions has a lattice structure, while the remaining directions have a continuum structure. The resulting semicontinuum problem describes the percolation of overlapping shapes in parallel layers or lanes with positional constraints for the placement of the objects along the discrete directions. Several semicontinuum percolation systems are analyzed like hypercuboids with a particular focus on 2D and 3D cases, disks, and parallelograms. Adapting the excluded volume arguments to the semicontinuum setting, we show that for the semicontinuum problem of hypercuboids, for fixed side-lengths of the hypercuboids along the directions in which a lattice structure is maintained, the percolation threshold is always independent of the side-lengths along the continuum directions. The result holds even when there is a distribution for the side-lengths along the continuum directions. Trends in the variation of the thresholds, as we vary the linear measure of the shapes along the continuum directions, are obtained for other semicontinuum models like disks and parallelograms in 2D. The results are compared with those of corresponding continuum and lattice models. For the 2D and 3D models considered, using Monte Carlo simulations, we verify the excluded volume predictions for the trends and numerical values of the percolation thresholds. Very good agreement is seen between the predicted numerical values and the simulation results. The semicontinuum setting also allows us to establish a connection between the percolation problem of overlapping shapes in 2D continuum and triangular lattice. We also verify that the isotropy of the threshold for anisotropic shapes and standard percolation universality class is maintained in the semicontinuum setting., Comment: 13 pages, 11 figures, 7 tables

We study the problem of a run and tumble particle in a harmonic trap, with a finite run and tumble time, by a direct integration of the equation of motion. An exact 1D steady state distribution, diagram laws and a programmable Volterra difference equation are derived to calculate any order of moments in any other dimension, both for steady state as well as the Laplace transform in time for the intermediate states. We also use the moments to infer the distribution by considering a Gaussian quadrature for the corresponding measure, and from the scaling law of high order moments., Comment: 12 pages 5 figures

Relaxation rates provide important characteristics both for classical and quantum processes. Essentially they control how fast the system thermalizes, equilibrates, {decoheres, and/or dissipates}. Moreover, very often they are directly accessible to be measured in the laboratory and hence they define key physical properties of the system. Experimentally measured relaxation rates can be used to test validity of a particular theoretical model. Here we analyze a fundamental question: {\em does quantum mechanics provide any nontrivial constraint for relaxation rates?} We prove the conjecture formulated a few years ago that any quantum channel implies that a maximal rate is bounded from above by the sum of all the relaxation rates divided by the dimension of the Hilbert space. It should be stressed that this constraint is universal (it is valid for all quantum systems with finite number of energy levels) and it is tight (cannot be improved). In addition, the constraint plays an analogous role to the seminal Bell inequalities and the well known Leggett-Garg inequalities (sometimes called temporal Bell inequalities). Violations of Bell inequalities rule out local hidden variable models, and violations of Leggett-Garg inequalities rule out macrorealism. Similarly, violations of the bound rule out completely positive-divisible evolution., Comment: 16 pages, no figures

The behavior of lattice models in which time reversibility is enforced at the level of trajectories (microscopic reversibility) is studied analytically. Conditions for ergodicity breaking are explored, and a few examples of systems characterized by an additional conserved quantity besides energy are presented. All the systems are characterized by ergodicity restoration when put in contact with a thermal bath, except for specific choices of the interactions between the atoms in the system and the bath. The study shows that the additional conserved quantities return to play a role in non-equilibrium conditions, with behaviors similar to those of some mesoscale systems, in which the transition rates satisfy detailed balance but not microscopic reversibility., Comment: 11 page, 4 figures

In this paper, we investigate the phase behaviors and dynamics of self-propelled particles with active reorientation in double-well potential. We observe the self-propelled particles exhibit flocking and clustering in an asymmetric potential trap. By MD simulations, we obtain a phase diagram of flocking with active reorientation and potential asymmetry as parameters. We compare the responses of inactive and active particles to the potential. It shows that active reorientation of particles amplifies the degree of aggregation on one side in the asymmetric potential well. Furthermore, we calculate the mean squared displacement and identify distinct diffusion regimes. These results highlight active particles with active reorientation exhibit greater sensitivity in double-well potentials., Comment: 7 pages, 8 figures

For a Markov and stationary stochastic process described by the well-known classical master equation, we introduce complex transition rates instead of real transition rates to study the pre-thermal oscillatory behaviour in complex probabilities. Further, for purely imaginary transition rates we obtain persistent infinitely long lived oscillations in complex probability whose nature depends on the dimensionality of the state space. We also take a peek into cases where we perturb the relaxation matrix for a dichotomous process with an oscillatory drive where the relative sign of the angular frequency of the drive decides whether there will be dissipation in the complex probability or not., Comment: 6 pages, 4 figures

We propose two new kinds of infinite resistor networks based on the Fibonacci sequence: a serial association of resistor sets connected in parallel (type 1) or a parallel association of resistor sets connected in series (type 2). We show that the sequence of the network's equivalent resistance converges uniformly in the parameter $\alpha=\frac{r_2}{r_1} \in [0,+\infty)$, where $r_1$ and $r_2$ are the first and second resistors in the network. We also show that these networks exhibit self-similarity and scale invariance, which mimics a self-similar fractal. We also provide some generalizations, including resistor networks based on high-order Fibonacci sequences and other recursive combinatorial sequences.

Many first-passage processes in complex media and related diffusion-controlled reactions can be described by means of eigenfunctions of the mixed Steklov-Neumann problem. In this paper, we investigate this spectral problem in a common setting when a small target or escape window (with Steklov condition) is located on the reflecting boundary (with Neumann condition). We start by inspecting two basic settings: an arc-shaped target on the boundary of a disk and a spherical-cap-shaped target on the boundary of a ball. We construct the explicit kernel of an integral operator that determines the eigenvalues and eigenfunctions and deduce their asymptotic behavior in the small-target limit. By relating the limiting kernel to an appropriate Dirichlet-to-Neumann operator, we extend these asymptotic results to other bounded domains with smooth boundaries. A straightforward application to first-passage processes is presented; in particular, we revisit the small-target behavior of the mean first-reaction time on perfectly or partially reactive targets, as well as for more sophisticated surface reactions that extend the conventional narrow escape problem.

The response of ionic solutions to time-varying electric fields, quantified by a frequency-dependent conductivity, is essential in many electrochemical applications. Yet, it constitutes a challenging problem due to the combined effect of Coulombic interactions, hydrodynamics, and thermal fluctuations. Here, we study the frequency-dependent conductivity of ionic solutions using a stochastic density functional theory. In the limit of small concentrations, we recover the classical Debye and Falkenhagen (DF) result, predicting an increase in conductivity with field frequency. At higher concentrations, we use a modified Coulomb interaction potential that accounts for the hard-core repulsion between the ions, which was recently employed in the zero-frequency case. Consequently, we extend the DF result to concentrated electrolytes. We discuss experimental and numerical studies and the complexity of observing the DF effect in such setups., Comment: 11 pages, 6 figures

This work presents a comparative study of the best models available to describe granular fluids in order to investigate the extent to which it makes sense to speak about a liquid-gas transition in a system of particles that present no attractive interactions. It is shown that the gas and the liquid correspond to regimes with clearly distinct rheological responses. A microscopic interpretation of what happens at the transition in terms of the time scales relevant to the various physical processes is also presented and put the test against numerical data. Our work calls for more experiments to test our predictions on real systems., Comment: 20 pages, 28 figures

We apply a state-of-the-art difference-in-differences approach to estimate the impact of ChatGPT's release on the writing style of condensed matter papers on arXiv. Our analysis reveals a statistically significant improvement in the English quality of abstracts written by non-native English speakers. Importantly, this improvement remains robust even after accounting for other potential factors, confirming that it can be attributed to the release of ChatGPT. This indicates widespread adoption of the tool. Following the release of ChatGPT, there is a significant increase in the use of unique words, while the frequency of rare words decreases. Across language families, the changes in writing style are significant for authors from the Latin and Ural-Altaic groups, but not for those from the Germanic or other Indo-European groups., Comment: 9 pages, 1 figure, 7 tables

The imposition of a global constraint of the conservation of total kinetic energy on a forced-dissipative Burgers equation yields a governing equation that is invariant under the time-reversal symmetry operation, $\{\mathcal{T}: t \to -t; u \to -u \}$, where $u$ is the velocity field. Moreover, the dissipation term gets strongly modified, as the viscosity is no longer a constant, but a fluctuating, state dependent quantity, which can even become negative in certain dynamical regimes. Despite these differences, the statistical properties of different dynamical regimes of the time-reversible Burgers equation and the standard forced-dssipative Burgers equation are equivalent, \`a la Gallavotti's conjecture of \textit{equivalence of nonequilibrium ensembles}. We show that the negative viscosity events occur only in the thermalized regime described by the time-reversible equation. This quasi-equilibrium regime is examined by calculating the local Lyapunov spectra and fluctuation relations. A pairing symmetry among the spectra is observed, indicating that the dynamics is chaotic and has an attractor spanning the entire phase space of the system. The violations of the second law of thermodynamics are found to be in accordance with the fluctuation relations, namely the Gallavotti-Cohen relation based on the phase-space contraction rate and the Cohen-Searles fluctuation relation based on the energy production rate. It is also argued that these violations are associated with the effects of the Galerkin-truncation, the latter is responsible for the thermalization.

Experiments using the Surface Force Apparatus have found anomalously long-ranged interactions between charged surfaces in concentrated salt solutions. Meanwhile, theory and simulations have suggested ion clustering to be the possible origin of this behaviour. The popular Restricted Primitive Model of electrolyte solutions, in which the solvent is represented by a uniform relative dielectric screening factor, $\varepsilon_r$, is unable to resolve the anomalous underscreening observed in experiments. In this work, we modify the Restricted Primitive Model to account for local dielectric saturation within the ion hydration shell. The dielectric screening factor in our model locally decreases from the bulk value to a lower saturated value at the ionic surface. The parameters for the model are deduced so that typical salt solubilities are obtained. Our simulations for both bulk and slit geometries show that our model displays strong cluster formation and these give rise to long-ranged interactions between charged surfaces at distances similar to what has been observed in SFA measurements. An electrolyte model wherein the dielectric screening factor remains uniform does not display similar clusters, even with unreasonably low values of $\varepsilon_r$.

We perform a numerical study of the kinetic Blume-Capel (BC) model to find if it exhibits the metamagnetic anomalies previously observed in the kinetic Ising model for supercritical periods. We employ a heat-bath Monte Carlo (MC) algorithm on a square lattice in which spins can take values of $\pm 1, 0$, with a non-zero crystal field, subjected to a sinusoidal oscillating field in conjunction with a constant bias. In the ordered region, we find an equivalent hysteretic response of the order parameters with its respective conjugate fields between the kinetic and the equilibrium model. In the disordered region (supercritical periods), we observed two peaks, symmetrical with respect to zero bias, in the susceptibility and scaled variance curves, consistent with the numerical and experimental findings on the kinetic Ising model. This behavior does not have a counterpart in the equilibrium model. Furthermore, we find that the peaks occur at higher values of the bias field and become progressively smaller as the density of zeros, or the amplitude of the oscillating field, increases. Using nucleation theory, we demonstrate that these fluctuations, as in the Ising model, are not a critical phenomenon, but that they are associated with a crossover between a single-droplet (SD) and a multi-droplet (MD) magnetization switching mechanism. For strong (weak) bias, the SD (MD) mechanism dominates. We also found that the zeros concentrate on the droplets' surfaces, which may cause a reduced interface tension in comparison with the Ising model . Our results suggest that metamagnetic anomalies are not particular to the kinetic Ising model, but rather are a general characteristic of spin kinetic models, and provide further evidence that the equivalence between dynamical phase transitions and equilibrium ones is only valid near the critical point., Comment: 33 pages, 11 figures

The limit of energy saving in the control of small systems has recently attracted much interest due to the concept refinement of the Maxwell demon. Inspired by a newly proposed set of fluctuation theorems, we report the first experimental verification of these equalities and inequalities in a ultracold 40Ca ion system, confirming the intrinsic nonequilibrium in the system due to involvement of the demon. Based on elaborately designed demon-involved control protocols, such as the Szilard engine protocol, we provide experimentally quantitative evidence of the dissipative information, and observe tighter bounds of both the extracted work and the demon's efficacy than the limits predicted by the Sagawa-Ueda theorem. Our results substantiate a close connection between the physical nature of information and nonequilibrium processes at the microscale, which help further understanding the thermodynamic characteristics of information and the optimal design of nanoscale and smaller systems.

Quantum thermometry refers to the study of measuring ultra-low temperatures in quantum systems. The precision of such a quantum thermometer is limited by the degree to which temperature can be estimated by quantum measurements. More precisely, the maximal precision is given by the inverse of the quantum Fisher information. In the present analysis, we show that quantum thermometers that are described by nonlinear Schr\"odinger equations allow for a significantly enhanced precision, that means larger quantum Fisher information. This is demonstrated for a variety of pedagogical scenarios consisting of single and two-qubits systems. The enhancement in precision is indicated by non-vanishing quantum speed limits, which originate in the fact that the thermal, Gibbs state is typically not invariant under the nonlinear equations of motion., Comment: 9 pages, 4 figures

Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a switching mechanism. Specifically, we obtain an exact expression of the Laplace-transformed characteristic function of the particle's position. Then, the characteristic function is used to compute the effective diffusion coefficient of a system performing intermittent dynamics. Further, we employ two examples: 1) Generalized run-and-tumble active particle, and 2) an active particle switching its dynamics between generalized active run-and-tumble motion and passive Brownian motion. In each case, explicit computations of the spatial cumulants are presented. Our findings reveal that the particle's position probability density function exhibit rich behaviours due to intermittent activity. Numerical simulations confirm our findings.

Enzymes are nano-scale machines that have evolved to drive chemical reactions out of equilibrium in the right place at the right time. Thermodynamically favourable reactions such as ATP hydrolysis are used by the cell to convert chemical energy into useful structure, function, and mechanical work. This includes the `fuelled' catalysis of chemical reactions that would otherwise be thermodynamically unfavourable. Given the complexity and specificity of enzymatic function, bottom-up design of enzymes presents a daunting task that is far more challenging than making passive molecules with specific binding affinities or building nano-scale mechanically active devices. Here, we present a thermodynamically-consistent model for the operation of such a fuelled enzyme, which uses the energy from a favourable reaction to undergo non-equilibrium conformational changes that in turn catalyze a chemical reaction on an attached substrate molecule. We show that enzymatic function can emerge through a bifurcation upon appropriate implementation of momentum conservation on the effective reaction coordinates of the low dimensional description of the enzyme, and thanks to a generically present dissipative coupling. By considering the different aspects of the dynamics, such as the interplay of the non-equilibrium drive and the geometry of the enzyme-substrate complex, we propose three golden rules that should be universally applicable for de novo design of enzymes, as they are based on generic ingredients and physical constraints. These rules lead to optimal combinations of parameters, which can vastly accelerate reactions, while at the same time decreasing the energy dissipation of the combined reaction process, or, in other words, to an efficient enzyme. Our results can complement the recently developed strategies for de novo enzyme design based on machine learning approaches.

Quantum decoherence is the effect that bridges quantum physics to well-understood classical physics. As such, it plays a crucial role in understanding the mysterious nature of quantum physics represented by Schr\"odinger's cat, for example. Quantum decoherence is also a source of quantum noise that has to be well under control in quantum computing and in various experiments based on quantum technologies. Here we point out that quantum decoherence can be captured by $\textit{complex}$ saddle points in the Feynman path integral in much the same way as quantum tunneling can be captured by instantons. In particular, we present some first-principle calculations in the Caldeira-Leggett model, which reproduce the predicted scaling behavior of quantum decoherence with respect to the parameters of the environment such as the temperature and the coupling to the system of interest. We also discuss how to extend our work to general models by Monte Carlo calculations using a recently developed method to overcome the sign problem., Comment: 5 pages, 3 figures

The entanglement of non-complementary regions is investigated in an inhomogeneous free-fermion chain through the lens of the fermionic logarithmic negativity. Focus is on the Krawtchouk chain, whose relation to the eponymous orthogonal polynomials allows for exact diagonalization and analytical calculations of certain correlation functions. For adjacent regions, the negativity scaling corresponds to that of a conformal field theory with central charge $c=1$, in agreement with previous studies on bipartite entanglement in the Krawtchouk chain. For disjoint regions, we focus on the skeletal regime where each region reduces to a single site. This regime is sufficient to extract the leading behaviour at large distances. In the bulk, the negativity decays as $d^{-4 \Delta_f}$ with $\Delta_f=1/2$, where $d$ is the separation between the regions. This is in agreement with the homogeneous result of free Dirac fermions in one dimension. Surprisingly, when one site is close to the boundary, this exponent changes and depends on the parity of the boundary site $m=0,1,2,\dots$, with $\Delta_f^{\textrm{even}}=3/8$ and $\Delta_f^{\textrm{odd}}=5/8$. The results are supported by numerics and analytical calculations., Comment: 20 pages, 8 figures

In a binary fluid mixture, the concentration gradient of a heavier molecular solute leads to a diffusive flux of solvent and solute to achieve thermodynamic equilibrium. If the solute concentration decreases with height, the system is always in a condition of stable mechanical equilibrium against gravity. We show experimentally that this mechanical equilibrium becomes unstable in case colloidal particles are dispersed uniformly within the mixture, and that the resulting colloidal suspension undergoes a transient convective instability with the onset of convection patterns. By means of a numerical analysis, we clarify the microscopic mechanism from which the observed destabilisation process originates. The solute concentration gradient drives an upward diffusiophoretic migration of colloids, in turn causing the development of a mechanically unstable layer within the sample, where the density of the suspension increases with height. Convective motions arise to minimize this localized rise in gravitational potential energy.

Coherent information quantifies the transmittable quantum information through a channel and is directly linked to the channel's quantum capacity. In the context of dynamical purification transitions, scrambling dynamics sustain extensive and positive coherent information at low measurement rates, but noises can suppress it to zero or negative values. Here we introduce quantum-enhanced operations into a noisy monitored quantum circuit. This circuit, viewed as a quantum channel, undergoes a phase transition in coherent information from a recoverable phase with positive values to an irrecoverable phase with negative values. This transition is modulated by the relative frequency of noise and quantum-enhanced operations. The existence of a recoverable phase implies that quantum-enhanced operations can facilitate reliable quantum information transmission in the presence of diverse noises. Remarkably, we propose a resource-efficient protocol to characterize this phase transition, effectively avoiding post-selection by utilizing every run of the quantum simulation. This approach bridges the gap between theoretical insights and practical implementation, making the phase transition feasible to demonstrate on realistic noisy intermediate-scale quantum devices.

We investigate the monitored quantum dynamics of Gaussian mixed states and derive the universal Fokker-Planck equations that govern the stochastic time evolution of entire density-matrix spectra, obtaining their exact solutions. From these equations, we reveal an even-odd effect in purification dynamics: whereas entropy exhibits exponential decay for an even number $N$ of complex fermions, algebraic decay with divergent purification time occurs for odd $N$ as a manifestation of dynamical criticality. Additionally, we identify the universal fluctuations of entropy in the chaotic regime, serving as a non-unitary counterpart of the universal conductance fluctuations in mesoscopic electronic transport phenomena. Furthermore, we elucidate and classify the universality classes of non-unitary quantum dynamics based on fundamental symmetry. We also validate the universality of these analytical results through extensive numerical simulations across different types of models.

Variable selection is a problem of statistics that aims to find the subset of the $N$-dimensional possible explanatory variables that are truly related to the generation process of the response variable. In high-dimensional setups, where the input dimension $N$ is comparable to the data size $M$, it is difficult to use classic methods based on $p$-values. Therefore, methods based on the ensemble learning are often used. In this review article, we introduce how the performance of these ensemble-based methods can be systematically analyzed using the replica method from statistical mechanics when $N$ and $M$ diverge at the same rate as $N,M\to\infty, M/N\to\alpha\in(0,\infty)$. As a concrete application, we analyze the power of stability selection (SS) and the derandomized knockoff (dKO) with the $\ell_1$-regularized statistics in the high-dimensional linear model. The result indicates that dKO provably outperforms the vanilla knockoff and the standard SS, while increasing the bootstrap resampling rate in SS might further improve the detection power., Comment: 25 pages, 4 figures, 1 table