Work extractable from quantum systems can be viewed as a resource to perform some tasks. Here, we try to relate the work extractable to some resource theory. To do this, we consider completely passive states and passive states as free states and, by identifying the free operations, formulate resource theories where the maximum work extractable is a monotone. In particular, we study how the free operations act on the free states, showing how a sort of temperature plays a pivotal role in these resource theories.

Stochastic resetting has recently emerged as a proficient strategy to reduce the completion time for a broad class of first-passage processes. In the canonical setup, one intermittently resets a given system to its initial configuration only to start afresh and continue evolving in time until the target goal is met. This is, however, an instantaneous process and thus less feasible for any practical purposes. A crucial generalization in this regard is to consider a finite-time return process which has significant ramifications to the firstpassage properties. Intriguingly, it has recently been shown that for diffusive search processes, returning in finite but stochastic time can gain significant speedup over the instantaneous resetting process. Unlike diffusion which has a diverging mean completion time, in this paper, we ask whether this phenomena can also be observed for a first-passage process with finite mean completion time. To this end, we explore the setup of a classical drift-diffusive search process in one dimension with stochastic resetting and further assume that the return phase is modulated by a potential $U\left(x\right)=\lambda \left|x\right|$ with $\lambda >0$. For this process, we compute the mean first-passage time exactly and underpin its characteristics with respect to the resetting rate and potential strength. We find a unified phase space that allows us to explore and identify the system parameter regions where stochastic return supersedes over both the underlying process and the process under instantaneous resetting. Furthermore and quite interestingly, we find that for a range of parameters the mean completion time under stochastic return protocol can be reduced further than the optimally restarted instantaneous processes. We thus believe that resetting with stochastic returns can serve as a better optimization strategy owing to its dominance over classical first passage under resetting.

We explore chimera states in a ring of nonlocally coupled type-I excitable phase oscillators, with each isolated oscillator being restricted to a homogeneous equilibrium state. Our study identifies the presence of breathing chimera states, characterized by their oscillatory dynamics and periodic fluctuations in the global order parameter. Beyond the breathing chimera states with a single coherent cluster, we find the $2n$-cluster breathing chimera states, where $2n$ represents an even number of coherent clusters. These states exhibit the varying phase difference between adjacent clusters and a consistent phase among clusters separated by one intermediate cluster. The number of clusters is found to be modulated by the relative coupling radius. These dynamics for the finite number of oscillators are well confirmed by the Ott-Antonsen ansatz.

The Kullback-Leibler cluster entropy ${\mathcal{D}}_{\mathcal{C}}[P\parallel Q]$ is evaluated for the empirical and model probability distributions $P$ and $Q$ of the clusters formed in the realized volatility time series of five assets (S&P500, NASDAQ, DJIA, DAX, and FTSEMIB). The Kullback-Leibler functional ${\mathcal{D}}_{\mathcal{C}}[P\parallel Q]$ provides complementary perspectives about the stochastic volatility process compared to the Shannon functional ${\mathcal{S}}_{\mathcal{C}}\left[P\right]$. While ${\mathcal{D}}_{\mathcal{C}}[P\parallel Q]$ is maximum at the short timescales, ${\mathcal{S}}_{\mathcal{C}}\left[P\right]$ is maximum at the large timescales leading to complementary optimization criteria tracing back respectively to the maximum and minimum relative entropy evolution principles. The realized volatility is modelled as a time-dependent fractional stochastic process characterized by power-law decaying distributions with positive correlation ($H>1/2$). As a case study, we build a multiperiod portfolio on diversity indexes derived from the Kullback-Leibler entropy measure of the realized volatility. The portfolio is robust and exhibits better performances over the horizon periods. A comparison with the portfolio built either according to the uniform distribution or in the framework of the Markowitz theory is also reported.

The notion of structural heterogeneity is pervasive in real networks, and their community organization is no exception. Still, a vast majority of community detection methods assume neatly hierarchically organized communities of a characteristic scale for a given hierarchical level. In this work, we demonstrate that the reality of scale-dependent community reorganization is convoluted with simultaneous processes of community splitting and merging, challenging the conventional understanding of community-scale adjustment. We provide a mathematical argument concerning the modularity function, the results from real-network analysis, and a simple network model for a comprehensive understanding of the nontrivial community reorganization process. The reorganization is characterized by a local drop in the number of communities as the resolution parameter varies. This study suggests a need for a paradigm shift in the study of network communities, which emphasizes the importance of considering scale-dependent reorganization to better understand the genuine structural organization of networks.

Collective motion in nature, from the murmurations of starlings to firefly flashes, showcases a remarkable level of self-organization. Swarmalator models are an emerging paradigm for describing collective behavior of oscillators which sync and swarm. Traditionally, most studies have focused on the self-organizing dynamics of swarmalators with continuous coupling. However, a key aspect of many biological systems, pulsed interactions, remains unexplored within the framework of swarmalators. In this paper, we analyze the collective behavior of pulse-coupled swarmalators with different characteristics of pulse and phase response curves. We report several collective states facilitated by the pulsatile interactions including bump state, active bump state, partial synchronized state, radial wave state, and death state. The stationary nature of spatial and phase dynamics characterizes the death state. Further, we provide an analytical estimate for the threshold coupling strength for the death state's existence by analyzing the minimal model's dynamics with two coupled swarmalators.

Disordered systems theory provides powerful tools to analyze the generic behaviors of high-dimensional systems, such as species-rich ecological communities or neural networks. By assuming randomness in their interactions, universality ensures that many microscopic details are irrelevant to system-wide dynamics; but the choice of a random ensemble still limits the generality of results. We show here, in the context of ecological dynamics, that these analytical tools do not require a specific choice of ensemble and that solutions can be found based only on a fundamental rotational symmetry in the interactions, encoding the idea that traits can be recombined into new species without altering global features. Dynamical outcomes then depend on the spectrum of the interaction matrix as a free parameter, allowing us to bridge between results found in different models of interactions and extend beyond them to previously unidentified behaviors. The distinctive feature of ecological models is the possibility of species extinctions, which leads to an increased universality of dynamics as the fraction of extinct species increases. We expect these findings can inform new developments in theoretical ecology as well as other families of complex systems.

Polyelectrolyte brushes consist of a set of charged linear macromolecules, each tethered at one end to a surface. An example is the glycocalyx which refers to hair-like negatively charged sugar molecules that coat the outside membrane of all cells. We consider the transport and equilibrium distribution of ions and the resulting electrical potential when such a brush is immersed in a salt buffer containing monovalent cations (sodium and/or potassium). The Gouy-Chapman model for ion screening at a charged surface captures the effects of the Coulombic force that drives ion electrophoresis and diffusion but neglects non-Coulombic forces and ion pairing. By including the distinct binding affinities of these counter-ions with the brush and their so-called Born radii, which account for Born forces acting on them when the permittivity is nonuniform, we propose modified Poisson-Nernst-Planck continuum models that show the distinct profiles that may result depending on those ion-specific properties.

Cellular migration is crucial for biological processes, including embryonic development, immune response, and wound healing. The myosin-clutch model is a framework that describes how cells control migration through the interactions between myosin, the clutch mechanism, and the substrate. This model is related to how cells regulate adhesion, generate traction forces, and move on compliant substrates. In this study, we present a five-dimensional nonlinear autonomous system to investigate the influences of myosin, clutches, substrate, and external load on the system's stability. Moreover, we analyze the effects of various parameters on fixed points and explore the frequency and amplitude of the limit cycle associated with oscillations. We discovered that the system demonstrates oscillatory behavior when the velocity of the myosin motor is relatively low or when the ratio of motor attachment rate to motor detachment rate is relatively high. The external load shares a fraction of the force exerted by myosin motors, thereby diminishing the force endured by the clutches. Within a specific range, an increase in external load not only diminishes and eventually eliminates the region lacking fixed points but also decelerates clutch detachment, enhancing clutch protein adherence.

Amyloid-beta ($\mathrm{A}\beta$) peptides and calcium ions (${\mathrm{Ca}}^{2+}$) serve critical roles in various physiological processes inside neurons, but their dysregulation is involved in the development of neurological disorders, including Alzheimer's disease. Particularly, $\mathrm{A}{\beta }_{42}$ peptides alter ${\mathrm{Ca}}^{2+}$ homeostasis, resulting in synaptic dysfunction and neuronal damage. On the other hand, ${\mathrm{Ca}}^{2+}$ ions can affect $\mathrm{A}\beta$ aggregation and clearance routes, either worsening or improving AD pathogenesis. We have considered a deterministic model for $\mathrm{A}\beta \text{−}{\mathrm{Ca}}^{2+}$ interaction and studied its noise-induced dynamics. The stochastic sensitivity analysis helps to find the confidential ellipses for the stable attractors of the stochastic system. In addition, we have developed a network model based on the interaction between $\mathrm{A}\beta$ peptides and ${\mathrm{Ca}}^{2+}$ ions to comprehend their dynamics in the brain connectome better. The probabilistic evolution approach characterizes the dynamics of the stochastic network model and estimates the potentials required to escape from one attractor to another. The numerical simulations suggest that the more connected node requires more energy to switch its state, and the noise intensity plays a crucial role in such cases. Furthermore, this study reveals that external perturbations on $\mathrm{A}\beta \text{−}{\mathrm{Ca}}^{2+}$ dynamics uncover novel targets for drug development and provide insights into the complex interplay between protein misfolding and synaptic dysfunction in Alzheimer's disease pathology.

Adhesion between cells plays an important role in many biological processes such as tissue morphogenesis and homeostasis, wound healing, and cancer cell metastasis. From a mathematical perspective, adhesion between multiple cell types has been previously analyzed using discrete and continuum models, including the cellular Potts models and partial differential equations (PDEs). While these models can represent certain biological situations well, cellular Potts models can be computationally expensive, and continuum models capture only the macroscopic behavior of a population of cells, ignoring stochasticity and the discrete nature of cell dynamics. Cellular automaton models allow us to address these problems and can be used for a wide variety of biological systems. In this paper we consider a cellular automaton approach and develop an on-lattice agent-based model (ABM) for cell migration and adhesion in a population composed of two cell types. By deriving and comparing the corresponding PDEs to the ABM, we demonstrate that cell aggregation and cell sorting are not possible in the PDE model. Therefore, we propose a set of discrete mean equations which better capture the behavior of the ABM in one and two dimensions.

The motion of microorganisms in complex fluids stands out as a prominent subject within fluid mechanics. In our study, we utilize the fictitious domain method to investigate the locomotion of squirmers along a convex wall in Giesekus viscoelastic fluids. This study examines the influence of fluid elasticity and wall curvature on squirmer particles, analyzing their movement patterns in detail. Near the convex wall, three distinct behavioral characteristics emerge: scattering, orbiting forward, and orbiting backward. The findings reveal that, compared with Newtonian fluids, squirmers exhibit a stronger tendency to be attracted toward the wall in viscoelastic fluids. This behavior is attributed to the elastic stress of the fluid, which generates a reverse torque on microbial particles, altering their movement direction and hindering their escape from the wall. Notably, as the wall curvature decreases, the likelihood of particles escaping diminishes.

We study the effects of conductivity variation on the Ponomarenko dynamo. Taking monotonically increasing, decreasing and sinusoidally varying radial profiles, we study the kinematic dynamo problem. The threshold of the dynamo, given by the critical magnetic Reynolds number ${\mathrm{Rm}}_c$, is found to strongly depend on the form of conductivity variation near the discontinuity of the velocity field where the shear is dominant. For monotonically varying profiles in the limit of sharp variation, this threshold maps to the problem of the dynamo with a jump in conductivity, while for the sinusoidal profile with large variations or wave numbers, the threshold increases due to effective diffusivity arising from the rapid changes in conductivity. Far from the threshold, it is found that the growth rate depends only on the local gradient of the conductivity near the discontinuity, with the opposite sign of shear and conductivity gradient leading to a larger growth rate, thereby aiding the dynamo instability in regenerating ${\mathrm{B}}_{\varphi }$ from ${\mathrm{B}}_r$. We calculate the expression for the growth rate in the limit of large $\text{Rm}(\gg 1)$ and find that the conductivity variation leads to a modification proportional to the local gradient of conductivity times ${\text{Rm}}^{-1/2}$. This correction is found to depend only on the local gradient of the conductivity at the discontinuity. Similar dependencies are found for realistic, smooth velocity profiles and for different magnetic boundary conditions.

The classical $X\mathrm{Y}$ model has been consistently studied since it was introduced more than six decades ago. Of particular interest has been the two-dimensional spin model's exhibition of the Berezinskii-Kosterlitz-Thouless (BKT) transition. This topological phenomenon describes the transition from bound vortex-antivortex pairs at low temperatures to unpaired or isolated vortices and antivortices above some critical temperature. In this work we propose a machine learning based method to determine the emergence of this phase transition. Generating unique states can be difficult due to the $U\left(1\right)$ symmetry present. We introduce an auxiliary field (analogous to a vortex density field) corresponding to a given state in order to eliminate the unwanted symmetry. An autoencoder was used to map these auxiliary fields into a lower-dimensional latent space. Samples were taken from this latent space to determine the thermal average of the vortex density, which was then used to determine the critical temperature of the phase transition.

Vibrated granular matter constitutes a useful system for studying the physics of active matter. Usually, self-propulsion is induced in grains through suitable asymmetry in the particle design. In this article we show that a symmetrical miniwheel placed on a vibrating plate self-propels along circular trajectories, showing chiral active dynamics. The chiral activity emerges through a sequence of spontaneous symmetry breaking in the particle's kinetics. The fact that isotropy, fore-aft, and chiral symmetries are broken spontaneously leads to distinct statistics, which include a temporal evolution involving stochastic resetting, a non-Gaussian velocity distribution with multiple peaks, broad power-law curvature distribution, and a bounded chirality probability, along with a phase transition from passive achiral to active chiral state as a function of vibration amplitude. Our study establishes the vibrated wheel as a three-state chiral active system that can serve as a model experimental system to study the nonequilibrium statistical mechanics and stochastic thermodynamics of chiral active systems and can inspire novel locomotion strategies in robotics.

Self-propelled particles that are subject to noise are a well-established generic model system for active matter. A homogeneous alignment field can be used to orient the direction of the self-propulsion velocity and to model systems like phoretic Janus particles with a magnetic dipole moment or magnetotactic bacteria in an external magnetic field. Computer simulations are used to predict the phase behavior and dynamics of self-propelled Brownian particles in a homogeneous alignment field in two dimensions. Phase boundaries of the gas-liquid coexistence region are calculated for various Péclet numbers, particle densities, and alignment field strengths. Critical points and exponents are calculated and, in agreement with previous simulations, do not seem to belong to the universality class of the 2D Ising model. Finally, the dynamics of spinodal decomposition for quenching the system from the one-phase to the two-phase coexistence region by increasing the Péclet number is characterized. Our results may help to identify parameters for optimal transport of active matter in complex environments.

In the study of quantum chaos diagnostics, considerable attention has been attributed to the Krylov complexity and the spectral form factor (SFF) for systems at infinite temperature. These investigations have unveiled universal properties of quantum chaotic systems. By extending the analysis to include the finite-temperature effects on the Krylov complexity and SFF, we demonstrate that the Lanczos coefficients $b_n$, which are associated with the Wightman inner product, display consistency with the universal hypothesis presented in Parker et al. [Phys. Rev. X 9, 041017 (2019)]. This result contrasts with the behavior of Lanczos coefficients associated with the standard inner product. Our results indicate that the slope $\alpha$ of the $b_n$ is bounded by $\pi k_{B}T$, where $k_B$ is the Boltzmann constant and $T$ is the temperature. We also investigate the SFF, which characterizes the two-point correlation of the spectrum and encapsulates an indicator of ergodicity denoted by $g$ in chaotic systems. Our analysis demonstrates that as the temperature decreases, the value of $g$ decreases as well. Considering that $\alpha$ also represents the operator growth rate, we establish a quantitative relationship between the ergodicity indicator and the Lanczos coefficients' slope. To support our findings, we provide evidence using the Gaussian orthogonal ensemble and a random spin model. Our work deepens the understanding of the finite-temperature effects on the Krylov complexity, the SFF, and the connection between ergodicity and operator growth.

In real systems, information is never delivered quickly and always will spread with a delay. Because of this delay, an event from the past influences the activities of another entity today, which is no guarantee of direct contact between the two. In certain ways, this can be the result of high-order interactions in which a direct connection is not always formed. In this paper, we look at how this delay affects the dynamics of Heider balance theory. We demonstrate that Heider balance with a delay as a third-order interaction is equivalent to fourth-order interactions or higher order but without the delay. Higher-order interaction is required by raising the value of delay. Our finding indicates that in the dynamics of Heider balance, increasing the delay period increases the order of interactions and the presence of imbalanced triangles even at temperatures close to zero.

Nontwist area–preserving maps violate the twist condition at specific orbits, resulting in shearless invariant curves that prevent chaotic transport. Plasmas and fluids with nonmonotonic equilibrium profiles may be described using nontwist systems, where even after these shearless curves break up, effective transport barriers persist, partially reducing transport coefficients. Some nontwist systems present multiple shearless curves in phase space, increasing the complexity of transport phenomena, which have not been thoroughly investigated until now. In this work, we examine the formation of effective transport barriers in a nontwist area–preserving mapping with multiple shearless transport barriers. By quantifying the effectiveness of each transport barrier in phase space, we identify two scenarios where particular barriers dominate over others. Our results also reveal configurations where the interplay of two transport barriers creates regions in phase space with significant orbit trapping, influencing overall transport dynamics.