This work develops a nonlinear and self-consistent framework for the single-mode simulation of TM-mode gyrotrons. Unlike TE modes, a nonlinear TM wave equation is derived by considering the additional axial modulation on the electron beam due to the interaction with the axial electric field. Together with the electrons' equations of motion, particle tracing simulation is conducted to model TM-mode oscillation. For a uniform structure, the electron-beam efficiency of the $\mathrm{T}{\mathrm{M}}_{11}$-mode gyrotron at the $W$ band can achieve 30% over broad parameter space. Its beam-current, beam-voltage, and pitch-factor tuning properties are investigated under different magnetic fields. By optimizing the interaction structure of the proposed gyrotron backward-wave oscillator (gyro-BWO), the maximum interaction efficiency is higher than 30% with a frequency tuning range of more than 6 GHz at the pitch factor of 1.5. The peak efficiency can remain high of 32% at low beam voltage (10 kV) and low magnetic field (32.8 kG), indicating additional operating conditions. These special features may facilitate the development of low-cost and compact gyrotron systems and show great potential in the applications for TM-mode gyro-BWOs.

Reconnection and turbulence are two of the most commonly observed dynamical processes in plasmas, but their relationship is still not fully understood. Using 2.5D kinetic particle-in-cell simulations of both strong turbulence and reconnection, we compare the cross-scale transfer of energy in the two systems by analyzing the generalization of the von Kármán Howarth equations for Hall magnetohydrodynamics, a formulation that subsumes the third-order law for steady energy transfer rates. Even though the large scale features are quite different, the finding is that the decomposition of the energy transfer is structurally very similar in the two cases. In the reconnection case, the time evolution of the energy transfer also exhibits a correlation with the reconnection rate. These results provide explicit evidence that reconnection dynamics fundamentally involves turbulence-like energy transfer.

The second law of thermodynamics is a statement about the statistics of the entropy production, $\langle \mathrm{\Sigma }\rangle \ge 0$. For small systems, it is known that the entropy production is a random variable and negative values ($\mathrm{\Sigma }<0$) might be observed in some experiments. This situation is sometimes called apparent violation of the second law. In this sense, how often is the second law violated? For a given average $\langle \mathrm{\Sigma }\rangle$, we show that the strong detailed fluctuation theorem implies a lower tight bound for the apparent violations of the second law. As applications, we verify that the bound is satisfied for the entropy produced in the heat exchange problem between two reservoirs mediated by a bosonic mode in the weak-coupling approximation, a levitated nanoparticle, and a classical particle in a box.

Inspired by the recent viral epidemic outbreak and its consequent worldwide pandemic, we devise a model to capture the dynamics and the universality of the spread of such infectious diseases. The transition from a precritical to the postcritical phase is modeled by a percolation problem driven by random walks on a two-dimensional lattice with an extra average number $\rho$ of nonlocal links per site. Using finite-size scaling analysis, we find that the effective exponents of the percolation transitions as well as the corresponding time thresholds, extrapolated to the infinite system size, are $\rho$ dependent. We argue that the $\rho$ dependence of our estimated exponents represents a crossover-type behavior caused by the finite-size effects between the two limiting regimes of the system. We also find that the universal scaling functions governing the critical behavior in every single realization of the model can be well described by the theory of extreme values for the maximum jumps in the order parameter and by the central limit theorem for the transition threshold.

Trilayered spin-1/2 Ising ferrimagnets are interesting thin systems for compensation phenomenon. In this work, a Metropolis Monte Carlo study is performed on the magnetic and thermodynamic response of such a system on square Bravais lattice, driven by uniform random external magnetic field with spatiotemporal variations. In two distinct configurations, the surface layers are made up of A and the middle layer is made up of B atoms in an ABA-type stacking while in AAB-type stacking, the top layer and the middle layer is made up of A atoms while the bottom layer is made up of B atoms. The magnetic coupling between the like atoms (A-A and B-B) is ferromagnetic while between the unlike atoms (A-B), it is antiferromagnetic. For the time-dependent external uniform random field, the mean is always set to zero and the standard deviation is varied until spin-field energy is comparable to the dominant cooperative energy of the system. The findings show that the observed compensation and critical points shift and steady-state magnetic behaviors shift among N, L, P, and Q, etc., type of ferrimagnetic behaviors, depending on the strength of external uniform random field. The compensation phenomenon even vanishes after crossing a finite threshold of standard deviation of the magnetic field for particular choices of the other controlling parameters. Thus islands of ferrimagnetic phase without compensation appear within the phase area with compensation of field-free case, in the two-dimensional Hamiltonian parameter space. For both the configurations, the areas of such islands even grow with increasing standard deviation of the external field, $\sigma$, obeying a scaling relation of the form: $f(\sigma ,A\left(\sigma \right))={\sigma }^{-b}A\left(\sigma \right)$ with $b_{\mathrm{ABA}}=1.958\pm 0.122$ and $b_{\mathrm{AAB}}=1.783\pm 0.118$.

We analyze the dynamical evolution of a fluid with nonlinear drag, for which binary collisions are elastic, described at the kinetic level by the Enskog-Fokker-Planck equation. This model system, rooted in the theory of nonlinear Brownian motion, displays a really complex behavior when quenched to low temperatures. Its glassy response is controlled by a long-lived nonequilibrium state, independent of the degree of nonlinearity and also of the Brownian-Brownian collisions rate. The latter property entails that this behavior persists in the collisionless case, where the fluid is described by the nonlinear Fokker-Planck equation. The observed response, which includes nonexponential, algebraic, relaxation, and strong memory effects, presents scaling properties: the time evolution of the temperature—for both relaxation and memory effects—falls onto a master curve, regardless of the details of the experiment. To account for the observed behavior in simulations, it is necessary to develop an extended Sonine approximation for the kinetic equation—which considers not only the fourth cumulant but also the sixth one.

Using a model heat engine, we show that neural-network-based reinforcement learning can identify thermodynamic trajectories of maximal efficiency. We consider both gradient and gradient-free reinforcement learning. We use an evolutionary learning algorithm to evolve a population of neural networks, subject to a directive to maximize the efficiency of a trajectory composed of a set of elementary thermodynamic processes; the resulting networks learn to carry out the maximally efficient Carnot, Stirling, or Otto cycles. When given an additional irreversible process, this evolutionary scheme learns a previously unknown thermodynamic cycle. Gradient-based reinforcement learning is able to learn the Stirling cycle, whereas an evolutionary approach achieves the optimal Carnot cycle. Our results show how the reinforcement learning strategies developed for game playing can be applied to solve physical problems conditioned upon path-extensive order parameters.

The space of connected graph partitions underlies statistical models used as evidence in court cases and reform efforts that analyze political districting plans. In response to the demands of redistricting applications, researchers have developed sampling methods that traverse this space, building on techniques developed for statistical physics. In this paper, we study connections between redistricting and statistical physics, and in particular with self-avoiding walks. We exploit knowledge of phase transitions and asymptotic behavior in self-avoiding walks to analyze two questions of crucial importance for Markov chain Monte Carlo analysis of districting plans. First, we examine mixing times of a popular Glauber dynamics-based Markov chain and show how the self-avoiding walk phase transitions interact with mixing time. We examine factors new to the redistricting context that complicate the picture, notably the population balance requirements, connectivity requirements, and the irregular graphs used. Second, we analyze the robustness of the qualitative properties of typical districting plans with respect to score functions and a certain lattice-like graph, called the state-dual graph, that is used as a discretization of geographic regions in most districting analysis. This helps us better understand the complex relationship between typical properties of districting plans and the score functions designed by political districting analysts. We conclude with directions for research at the interface of statistical physics, Markov chains, and political districting.

Parrondo's effect is a well-known apparent paradox where a combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's effect can occur not only in the case of one-dimensional discrete quantum walks with random or deterministic periodic sequence of two- or multistate quantum coins but also in the case of one-dimensional discrete quantum walks with deterministic aperiodic sequence of two-state quantum coins. Moreover, we show how Parrondo's effect affects the time evolution of the walker-coin quantum entanglement.

We study the energy dynamics of a particle in a billiard subject to a rapid periodic drive. In the regime of large driving frequencies $\omega$, we find that the particle's energy evolves diffusively, which suggests that the particle's energy distribution $\eta (E,t)$ satisfies a Fokker-Planck equation. We calculate the rates of energy absorption and diffusion associated with this equation, finding that these rates are proportional to ${\omega }^{-2}$ for large $\omega$. Our analysis suggests three phases of energy evolution: Prethermalization on short timescales, then slow energy absorption in accordance with the Fokker-Planck equation, and finally a breakdown of the rapid driving assumption for large energies and high particle speeds. We also present numerical simulations of the evolution of a rapidly driven billiard particle, which corroborate our theoretical results.

A biparametric family of hexagonal billiards enjoying the $C_3$ point symmetry is introduced and numerically investigated. First, the relative measure $r(\ell ,\theta ;t)$ in a reduced phase space was mapped onto the parameter plane $\ell \times \theta$ for discrete time $t$ up to ${10}^8$ and averaged in tens of randomly chosen initial conditions in each billiard. The resulting phase diagram allowed us to identify fully ergodic systems in the set. It is then shown that the absolute value of the position autocorrelation function decays like $|C_q\left(t\right)|\sim t^{-\sigma }$, with $0<\sigma ⩽1$ in the hexagons. Following previous examples of irrational triangles, we were able to find billiards for which $\sigma \sim 1$. This is further evidence that, although not chaotic (all Lyapunov exponents are zero), billiards in polygons might exhibit a near strongly mixing dynamics in the ergodic hierarchy. Quantized counterparts with distinct classical properties were also characterized. Spectral properties of singlets and doublets of the quantum billiards were investigated separately well beyond the ground state. As a rule of thumb, for both singlet and doublet sequences, we calculate the first 120 000 energy eigenvalues in a given billiard and compute the nearest neighbor spacing distribution $p\left(s\right)$, as well as the cumulative spacing function $I\left(s\right)={\int }_0^{s}p\left(s^{\prime }\right)d{s}^{\prime }$, by considering the last 20 000 eigenvalues only. For billiards with $\sigma \sim 1$, we observe the results predicted for chaotic geometries by Leyvraz, Schmit, and Seligman, namely, a Gaussian unitary ensemble behavior in the degenerate subspectrum, in spite of the presence of time-reversal invariance, and a Gaussian orthogonal ensemble behavior in the singlets subset. For $0<\sigma <1$, formulas for intermediate quantum statistics have been derived for the doublets following previous works by Brody, Berry and Robnik, and Bastistić and Robnik. Different regimes in a given energy spectrum have been identified through the so-called ergodic parameter $\alpha =t_H/t_C$, the ratio between the Heisenberg time and the classical diffusive-like transport time, which signals the possibility of quantum dynamical localization when $\alpha <1$. A good quantitative agreement is found between the appropriate formulas with parameters extracted from the classical phase space and the data from the calculated quantum spectra. A rich variety of standing wave patterns and corresponding Poincaré-Husimi representations in a reduced phase space are reported, including those associated with lattice modes, scarring, and high-frequency localization phenomena.

In attempts to manage spatiotemporal transient chaos in spatially extended systems, these systems are often subjected to protocols that perturb them as a whole and stabilize globally a new dynamic regime, as, for example, a uniform steady state. In this work we show that selectively perturbing only part of a system can generate space-time patterns that are not observed when controlling the whole system. Depending on the protocol used, these new patterns can emerge either in the perturbed or the unperturbed region. Specifically, we use a spatially localized time-delayed feedback scheme on the one-dimensional Gray-Scott reaction-diffusion system in the transient chaotic regime and demonstrate, through the numerical integration of the resulting kinetic equations, the stabilization of spatially localized space-time patterns that can be perfectly periodic. The mechanism underlying the observed pattern generation is related to diffusion across the interfaces separating the perturbed and unperturbed regions.

Liquid crystal elastomers contract along their director on heating and recover on cooling, offering great potential as actuators and artificial muscles. If a flat sheet is programed with a spatially varying director pattern, then it will actuate into a curved surface, allowing the material to act as a strong machine such as a grabber or lifter. Here we study the actuation of programed annular sheets which, owing to their central hole, can sidestep constraints on area and orientation. We systematically catalog the set of developable surfaces encodable via axisymmetric director patterns and uncover several qualitatively new modes of actuation, including cylinders, irises, and everted surfaces in which the inner boundary becomes the outer boundary after actuation. We confirm our designs with a combination of experiments and numerics. Many of our actuators can reattain their initial inner or outer radius upon completing actuation, making them particularly promising, as they can avoid potentially problematic stresses in their activated state even when fixed onto a frame or pipe.

In this work, the electrohydrodynamic instability induced by a unipolar charge injection is extended from a single-phase dielectric liquid to a two-phase system that consists of a liquid-air interface. A volume-of-fluid model-based two-phase solver was developed with simplified Maxwell equations implemented in the open-source platform OpenFOAM. The numerically obtained critical value for the linear stability matches well with the theoretical values. To highlight the effect of the slip boundary at interface, the deformation of the interface is ignored. A bifurcation diagram with hysteresis loop linking the linear and finite-amplitude criteria, which is $U_f=0.059$, was obtained in this situation. It is concluded that the lack of viscous effect at interface leads to a significant increase in the flow intensity, which is the reason for the smaller instability threshold in two-phase system. The presence of interface also changes the flow structure and results in a shear distribution of electric force, which may play an important role in the interface deformation.

Discontinuous phase transitions out of equilibrium can be characterized by the behavior of macroscopic stochastic currents. But while much is known about the average current, the situation is much less understood for higher statistics. In this paper, we address the consequences of the diverging metastability lifetime—a hallmark of discontinuous transitions—in the fluctuations of arbitrary thermodynamic currents, including the entropy production. In particular, we center our discussion on the conditional statistics, given which phase the system is in. We highlight the interplay between integration window and metastability lifetime, which is not manifested in the average current, but strongly influences the fluctuations. We introduce conditional currents and find, among other predictions, their connection to average and scaled variance through a finite-time version of large deviation theory and a minimal model. Our results are then further verified in two paradigmatic models of discontinuous transitions: Schlögl's model of chemical reactions, and a 12-state Potts model subject to two baths at different temperatures.

We present integrable models of interacting spin-1/2 chains which can be interpreted as hard-rod deformations of the XXZ Heisenberg chains. The models support multiple particle types: Dynamical hard rods of length $\ell$ and particles with lengths ${\ell }^{\prime }<\ell$ that are immobile except for the interaction with the hard rods. We encounter a remarkable phenomenon in these interacting models: Exact spectral degeneracies across different deformations and volumes. The algebraic integrability of these systems is also treated using a recently developed formalism for medium-range integrable spin chains. We present the detailed Bethe Ansatz solution for the case $\ell =2$.

Dynamical system theory has recently shown promise for uncovering causality and directionality in complex systems, particularly using the method of convergent cross mapping (CCM). In spite of its success in the literature, the presence of process noise raises concern about CCM's ability to uncover coupling direction. Furthermore, CCM's capacity to detect indirect causal links may be challenged in simulated unidrectionally coupled Rossler-Lorenz systems. To overcome these limitations, we propose a method that places a Gaussian process prior on a cross mapping function (named GP-CCM) to impose constraints on local state space neighborhood comparisons. Bayesian posterior likelihood and evidence ratio tests, as well as surrogate data analyses are performed to obtain a robust statistic for dynamical coupling directionality. We demonstrate GP-CCM's performance with respect to CCM in synthetic data simulation as well as in empirical electroencephelography (EEG) and functional near infrared spectroscopy (fNIRS) activity data. Our findings show that GP-CCM provides a statistic that consistently reports indirect causal structures in non-separable unidirectional system interactions; GP-CCM also provides coupling direction estimates in noisy physiological signals, showing that EEG likely causes, i.e., drives, fNIRS dynamics.

Conversion of temporal to spatial correlations in the cortex is one of the most intriguing functions in the brain. The learning at synapses triggering the correlation conversion can take place in a wide integration window, whose influence on the correlation conversion remains elusive. Here we propose a generalized associative memory model of pattern sequences, in which pattern separations within an arbitrary Hebbian length are learned. The model can be analytically solved, and predicts that a small Hebbian length can already significantly enhance the correlation conversion, i.e., the stimulus-induced attractor can be highly correlated with a significant number of patterns in the stored sequence, thereby facilitating state transitions in the neural representation space. Moreover, an anti-Hebbian component is able to reshape the energy landscape of memories, akin to the memory regulation function during sleep. Our work thus establishes the fundamental connection between associative memory, Hebbian length, and correlation conversion in the brain.

Associative memory is a fundamental function in the brain. Here, we generalize the standard associative memory model to include long-range Hebbian interactions at the learning stage, corresponding to a large synaptic integration window. In our model, the Hebbian length can be arbitrarily large. The spectral density of the coupling matrix is derived using the replica method, which is also shown to be consistent with the results obtained by applying the free probability method. The maximal eigenvalue is then obtained by an iterative equation, related to the paramagnetic to spin glass transition in the model. Altogether, this work establishes the connection between the associative memory with arbitrary Hebbian length and the asymptotic eigen-spectrum of the neural-coupling matrix.