Molecular expressions for thermodynamic properties and derivatives of the entropy up to third order in the adiabatic grand-isochoric $\mu VL$ and adiabatic grand-isobaric $\mu pR$ ensembles are systematically derived using the methodology developed by Lustig for the microcanonical and canonical ensembles [J. Chem. Phys. 100, 3048 (1994); Mol. Phys. 110, 3041 (2012)]. They are expressed by phase-space functions, which represent derivatives of the entropy with respect to the chemical potential, the volume, and the Hill energy $L$ in the $\mu VL$ ensemble and with respect to the chemical potential, the pressure, and the Ray energy $R$ in the $\mu pR$ ensemble. The derived expressions are validated for both ensembles by Monte Carlo simulations for the simple Lennard-Jones model fluid at three selected state points.

Although the plasma-induced receiving and radiating near-field cutoff phenomena in the subwavelength regime are found of crucial importance in electromagnetic (EM) signal transmissions and plasma property studies, their mechanisms to a large extent remain unclear and undistinguished. In this paper, in the perspective of field and energy transfer, it is demonstrated that the cutoff in the near-field regime is completely different from that in the geometric optical regime. Results show that, for the receiving mode, epsilon-near-zero (ENZ) plasmas can be treated as a nearly ideal EM fluid, and thus, EM waves are restricted into the plasma channel. For the radiating mode, on the other hand, it is the destructive interference between the electric dipole fields of the antenna and the ENZ plasma that results in vanishing far-field radiation. As an important supplement to the existing cutoff theories, our results not only offer clearer physical insights into the near-field cutoff effect but also provide a helpful reference for cutoff-related practical applications in various frequency bands.

We study the effects of redistributing superthermal electrons on bremsstrahlung radiation from hot relativistic plasma. We consider thermal and nonthermal distribution of electrons with an energy cutoff in the phase space and explore the impact of the energy cutoff on bremsstrahlung losses. We discover that the redistribution of the superthermal electrons into lower energies reduces radiative losses, which is in contrast to nonrelativistic plasma. Finally, we discuss the possible relevance of our results for open magnetic field line configurations and prospects of the aneutronic fusion based on proton-boron-11 (p-B11) fuel.

The harmonically confined Vicsek model displays qualitative and quantitative features observed in natural insect swarms. It exhibits a scale-free transition between single and multicluster chaotic phases. Finite-size scaling indicates that this unusual phase transition occurs at zero confinement [Phys. Rev. E 107, 014209 (2023)]. While the evidence of the scale-free-chaos phase transition comes from numerical simulations, here we present its mean-field theory. Analytically determined critical exponents are those of the Landau theory of equilibrium phase transitions plus dynamical critical exponent $z=1$ and a new critical exponent $\phi =0.5$ for the largest Lyapunov exponent. The phase transition occurs at zero confinement and noise in the mean-field theory. The noise line of zero largest Lyapunov exponents informs observed behavior: (i) the qualitative shape of the swarm (on average, the center of mass rotates slowly at the rate marked by the winding number and its trajectory fills compactly the space, similarly to the observed condensed nucleus surrounded by vapor) and (ii) the critical exponents resemble those observed in natural swarms. Our predictions include power laws for the frequency of the maximal spectral amplitude and the winding number.

We derive the general solution for counting the stationary points of mean-field complex landscapes. It incorporates Parisi's solution for the ground state, as it should. Using this solution, we count the stationary points of two models: one with multistep replica symmetry breaking and one with full replica symmetry breaking.

We construct climate networks based on surface air temperature data to identify distinct signatures of climatic phenomena such as El Niño and La Niña events, which trigger many climatic disruptions around the globe with severe economic and ecological consequences. The climate network has been seen to show a discontinuous phase transition in the size of the normalized largest cluster and the susceptibility during both events. The correlation matrix of the network shows a structure that has distinct characteristics for El Niño events, La Niña events, and normal conditions of the Pacific Ocean. We also identify the signatures of the El Niño southern oscillations in the heat map of the cross-correlation and network quantifiers like the betweenness centrality. The distribution of teleconnections of distinct strengths, the betweenness centrality distributions, and the geographic location of nodes of high betweenness centrality yield important insights into the structure of the network and the transfer of information between different parts. We further discuss the predictive power of these quantities.

We study the energy extraction from and charging to a finite-dimensional quantum system by general quantum operations. We prove that the changes in energy induced by unital quantum operations are limited by the ergotropy and charging bounds for unitary quantum operations. This implies that, in order to break the ergotropy bound for unitary quantum operations, one needs to perform a quantum operation with feedback control. We also show that the ergotropy bound for unital quantum operations, applied to initial thermal equilibrium states, is tighter than the inequality representing the standard second law of thermodynamics without feedback control.

The nucleation-growth process is a crucial component of crystallization. While previous theoretical models have focused on nucleation events and postnucleation growth, such as the classical nucleation theory and Lifshitz-Slyozov-Wagner model, recent advancements in experiments and simulations have highlighted the inability of classical models to explain the transient dynamics during the early development of nanocrystals. To address these shortcomings, we present a model that describes the nucleation-growth dynamics of individual nanocrystals as a series of reversible chain reactions, with the free energy landscape extended to include activation-adsorption-relaxation reaction pathways. By using the Monte Carlo method based on the transition state theory, we simulate the crystallization dynamics. We derive a Fokker-Planck formalism from the master equation to describe the nucleation-growth process as a heterogeneous random walk on the extended free energy landscape with activated states. Our results reveal the transient quasiequilibrium of the prenucleation stage before nucleation starts, and we identify a postnucleation crossover regime where the dynamic growth exponents asymptotically converge towards classical limits. Additionally, we generalize the power laws to address the dimension and scale effects for the growth of large crystals.

The out-of-time ordered correlator (OTOC) is a measure of scrambling of quantum information. Scrambling is intuitively considered to be a significant feature of chaotic systems, and thus, the OTOC is widely used as a measure of chaos. For short times exponential growth is related to the classical Lyapunov exponent, sometimes known as the butterfly effect. At long times the OTOC attains an average equilibrium value with possible oscillations. For fully chaotic systems the approach to the asymptotic regime is exponential, with a rate given by the classical Ruelle-Pollicott resonances. In this work, we extend this notion to the more generic case of systems with mixed dynamics, in particular using the standard map, and we are able to show that the relaxation to equilibrium of the OTOC is governed by generalized classical resonances.

We explore the statistics of assembling soft-matter building blocks to investigate the uptake and encapsulation of cargo particles by carriers engulfing their load. While the such carrier-cargo complexes are important for many applications out of equilibrium, such as drug delivery and synthetic cell encapsulation, we uncover here the basic statistical physics in minimal hard-core-like models for particle uptake. Introducing an exactly solvable equilibrium model in one dimension, we demonstrate that the formation of carrier-cargo complexes can be largely tuned by both the cargo concentration and the carriers' interior size. These findings are intuitively explained by interpreting the internal free space (partition function) of the cargo inside a carrier as its engulfment strength, which can be mapped to an external control parameter (chemical potential) of an additional effective particle species. Assuming a hard carrier membrane, such a mapping can be exactly applied to account for multiple cargo uptake involving various carrier or cargo species and even attractive uptake mechanisms, while soft interactions require certain approximations. We further argue that the Boltzmann occupation law identified within our approach is broken when particle uptake is governed by nonequilibrium forces. Speculating on alternative occupation laws using effective parameters, we put forward a Bose-Einstein-like phase transition associated with polydisperse carrier properties.

Elastic strips provide a general motif for studying shape transitions. When actuated through rotation of its boundaries, a buckled strip exhibits, depending on the direction of rotation, three types of shape transitions: buckling, algebraic snap-through, or exponential snap-through. The transition dynamics is linked to the character of the bifurcation, which, in turn, is disclosed by the normal form of the system, but deriving normal forms is challenging. Recent work has used asymptotic methods to obtain this form for algebraic snap-through, but, to date, there is no methodology for extending this analysis to other transitions. Here we introduce a method to analyze the dynamic characteristics of an elastic strip near a transition and extend, in a straightforward manner, the previously proposed asymptotic analysis to exponential snap-through and buckling transitions. Importantly, we show that these normal forms dictate all the dynamic characteristics of the elastic strip near a shape transition. Our analysis provides reliable tools to diagnose and anticipate elastic shape transitions.

We continue the work by Lennard-Jones and Ingham, and later by Kane and Goeppert-Mayer, and present a general lattice sum formula for the hexagonal close packed (hcp) structure with different $c/a$ ratios for the two lattice parameters $a$ and $c$ of the hexagonal unit cell. The lattice sum is expressed in terms of fast converging series of Bessel functions. This allows us to analytically examine the behavior of a Lennard-Jones potential as a function of the $c/a$ ratio. In contrast to the hard-sphere model, where we have the ideal ratio of $c/a=\sqrt{8/3}$ with 12 kissing spheres around a central atom, we observe the occurrence of a slight symmetry-breaking effect and the appearance of a second metastable minimum for the (12,6) Lennard-Jones potential around the ratio $c/a=2/3$. We also show that the analytical continuation of the $(n,m)$ Lennard-Jones potential to the domain $n,m<3$ such as the Kratzer potential ($n=2,m=1$) gives unphysical results.

With large-scale Monte Carlo simulations, we investigate the nonsteady relaxation at the dynamic depinning transition in the two-dimensional Gaussian random-field Ising model. The dynamic scaling behavior is carefully analyzed, and the transition fields as well as static and dynamic exponents are accurately determined based on the short-time dynamic scaling form. Different from the usual assumption, two distinguished growth processes of spatial correlation lengths for the velocity and height of the domain wall are found. Thus, the universality class of the depinning transition is established, which significantly differs from that of the quenched disorder equation but agrees with that of the recent experiment as well as other simulations works. Under the influence of the mesoscopic time regime, the crossover from the second-order phase transition to the first-order one is confirmed in the weak-disorder regime, yielding an abnormal disorder-dependent nature of the criticality.

We construct Arnol'd cat map lattice field theories in phase space and configuration space. In phase space we impose that the evolution operator of the linearly coupled maps be an element of the symplectic group, in direct generalization of the case of one map. To this end we exploit the correspondence between the cat map and the Fibonacci sequence. The chaotic properties of these systems also can be understood from the equations of motion in configuration space. These describe inverted harmonic oscillators, where the runaway behavior of the potential competes with the toroidal compactification of the phase space. We highlight the spatiotemporal chaotic properties of these systems using standard benchmarks for probing deterministic chaos of dynamical systems, namely, the complete dense set of unstable periodic orbits, which, for long periods, lead to ergodicity and mixing. The spectrum of the periods exhibits a strong dependence on the strength and the range of the interaction.

In some systems, the behavior of the constituent units can create a “context” that modifies the direct interactions among them. This mechanism of indirect modification inspired us to develop a minimal model of context-dependent spreading. In our model, agents actively impede (favor) or not diffusion during an interaction, depending on the behavior they observe among all the peers in the group within which that interaction occurs. We divide the population into two behavioral types and provide a mean-field theory to parametrize mixing patterns of arbitrary type-assortativity within groups of any size. As an application, we examine an epidemic-spreading model with context-dependent adoption of prophylactic tools such as face masks. By analyzing the distributions of groups' size and type-composition, we uncover a rich phenomenology for the basic reproduction number and the endemic state. We analytically show how changing the group organization of contacts can either facilitate or hinder epidemic spreading, eventually moving the system from the subcritical to the supercritical phase and vice versa, depending mainly on sociological factors, such as whether the prophylactic behavior is hardly or easily induced. More generally, our work provides a theoretical foundation to model higher-order contexts and analyze their dynamical implications, envisioning a broad theory of context-dependent interactions that would allow for a new systematic investigation of a variety of complex systems.

The rapid increase of population and settlement structures in the Global South during recent decades has motivated the development of suitable models to describe their formation and evolution. Such settlement formation has been previously suggested to be dynamically driven by simple pattern-forming mechanisms. Here, we explore the use of a data-driven white-box approach, called SINDy, to discover differential equation models directly from available spatiotemporal demographic data for three representative regions of the Global South. We show that the current resolution and observation time of the available data are insufficient to uncover relevant pattern-forming mechanisms in settlement development. Using synthetic data generated with a generic pattern-forming model, the Allen-Cahn equation, we characterize what the requirements are for spatial and temporal resolution, as well as observation time, to successfully identify possible model system equations. Overall, the study provides a theoretical framework for the analysis of large-scale geographical and/or ecological systems, and it motivates further improvements in optimization approaches and data collection.

Microswimmers can acquire information on the surrounding fluid by sensing mechanical queues. They can then navigate in response to these signals. We analyze this navigation by combining deep reinforcement learning with direct numerical simulations to resolve the hydrodynamics. We study how local and nonlocal information can be used to train a swimmer to achieve particular swimming tasks in a nonuniform flow field, in particular, a zigzag shear flow. The swimming tasks are (1) learning how to swim in the vorticity direction, (2) learning how to swim in the shear-gradient direction, and (3) learning how to swim in the shear-flow direction. We find that access to laboratory frame information on the swimmer's instantaneous orientation is all that is required in order to reach the optimal policy for tasks (1) and (2). However, information on both the translational and rotational velocities seems to be required to accomplish task (3). Inspired by biological microorganisms, we also consider the case where the swimmers sense local information, i.e., surface hydrodynamic forces, together with a signal direction. This might correspond to gravity or, for microorganisms with light sensors, a light source. In this case, we show that the swimmer can reach a comparable level of performance to that of a swimmer with access to laboratory frame variables. We also analyze the role of different swimming modes, i.e., pusher, puller, and neutral.

The time-asymptotic state of a finite-amplitude perturbation in a collisionless and Maxwellian plasma is typically represented as a steady state of two nonlinearly superposed, counterpropagating Bernstein-Greene-Kruskal (BGK) modes. Using high-resolution Vlasov-Poisson simulations, we show that the plasma evolves self-consistently into a time-asymptotic state of multiple vortexlike structures that gradually fill the phase space and reduce filamentation. This occurs without the need for external forcing or the presence of an energetic plasma population. This finding suggests that the time-asymptotic regime of the plasma is rather akin to a nonlinear superposition of multiple BGK-like modes associated with nearly constant phase-speed waves. The electric field and the space-averaged particle distribution function exhibit a power-law broad spectrum, which is consistent with an energy cascade towards smaller scales in both position and velocity spaces.

In quantum targeted energy transfer, bosons are transferred from a certain crystal site to an alternative one, utilizing a nonlinear resonance configuration similar to the classical targeted energy transfer. We use a computational method based on machine learning algorithms in order to investigate selectivity as well as efficiency of the quantum transfer in the context of a dimer and a trimer system. We find that our method identifies resonant quantum transfer paths that allow boson transfer in unison. The method is readily extensible to larger lattice systems involving nonlinear resonances.