Understanding magnetic field growth in astrophysical objects is a persistent challenge. In stars and galaxies, turbulent flows with net kinetic helicity are believed to be responsible for driving large-scale magnetic fields. However, numerical simulations have demonstrated that such helical dynamos in closed volumes saturate at lower magnetic field strengths when increasing the magnetic Reynolds number $\text{Rm}$. This would imply that helical large-scale dynamos cannot be efficient in astrophysical bodies without the help of helicity outflows such as stellar winds. But do these implications actually apply for very large $\text{Rm}$? Here we tackle the long-standing question of how much helical large-scale dynamo growth occurs independent of $\text{Rm}$ in a closed volume. We analyze data from numerical simulations with a new method that tracks resistive versus nonresistive drivers of helical field growth. We identify a presaturation regime when the large-scale field grows at a rate independent of $\text{Rm}$, but to an $\text{Rm}$-dependent magnitude. The latter $\text{Rm}$ dependence is due to a dominant resistive contribution, but whose fractional contribution to the large-scale magnetic energy decreases with increasing $\text{Rm}$. We argue that the resistive contribution would become negligible at large $\text{Rm}$ and an $\text{Rm}$-independent dynamical contribution would dominate if the current helicity spectrum in the inertial range is steeper than $k^0$. As such helicity spectra are plausible, this renews optimism for the relevance of closed dynamos. Our work pinpoints how modest $\text{Rm}$ simulations can cause misapprehension of the $\text{Rm}\to \infty$ behavior.

For classic systems, the thermodynamic uncertainty relation (TUR) states that the fluctuations of a current have a lower bound in terms of the entropy production. Some TURs are rooted in information theory, particularly derived from relations between observations (mean and variance) and dissimilarities, such as the Kullback-Leibler divergence, which plays the role of entropy production in stochastic thermodynamics. We generalize this idea for quantum systems, where we find a lower bound for the uncertainty of quantum observables given in terms of the quantum relative entropy. We apply the result to obtain a quantum thermodynamic uncertainty relation in terms of the quantum entropy production, valid for arbitrary dynamics and nonthermal environments.

In this paper we study a quantum Otto thermal machine where the working substance is composed of $N$ identical qubits coupled to a single mode of a bosonic field, where the atoms and the field interact with a reservoir, as described by the so-called open Dicke model. By controlling the relevant and experimentally accessible parameters of the model we show that it is possible to build a universal quantum heat machine (UQHM) that can function as an engine, refrigerator, heater, or accelerator. The heat and work exchanges are computed taking into account the growth of the number $N$ of atoms as well as the coupling regimes characteristic of the Dicke model for several ratios of temperatures of the two thermal reservoirs. The analysis of quantum features such as entanglement and second-order correlation shows that these quantum resources do not affect either the efficiency or the performance of the UQHM based on the open Dicke model. In addition, we show that the improvement in both efficiency and coefficient of performance of our UQHM occurs for regions around the critical value of the phase transition parameter of the model.

We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics. This fairly accurate qualitative description plausibly renders mean-field theory a reasonable approach for freezing in three dimensions. At the same time, our mean-field treatment itself suggests freezing to persist in infinitely many dimensions, as advanced from recent simulations [Charbonneau et al., Eur. Phys. J. E 44, 101 (2021)].

A simple transmission line composed of pulse-coupled units is presented. The model captures the basic properties of excitable media with, in particular, the robust transmission of information via traveling wave solutions. For rectified linear units with a cut-off threshold, the model is exactly solvable and analytical results on propagation are presented. The ability to convey a nontrivial message is studied in detail.

Only a few years have passed since the discovery of polar nematics, and now they are becoming the most actively studied liquid-crystal materials. Despite numerous breakthrough findings made recently, a theoretical systematization is still lacking. In the present paper, we take a step toward systematization. The powerful technique of molecular-statistical physics has been applied to an assembly of polar molecules influenced by electric field. Three polar nematic phases were found to be stable at various conditions: the double-splay ferroelectric nematic $N_F^{2D}$ (observed in the lower-temperature range in the absence of or at low electric field), the double-splay antiferroelectric nematic $N_{AF}$ (observed at intermediate temperature in the absence of or at low electric field), and the single-splay ferroelectric nematic $N_F^{1D}$ (observed at moderate electric field at any temperature below transition into paraelectric nematic $N$ and in the higher-temperature range (also below $N$) at low electric field or without it. A paradoxical transition from $N_F^{1D}$ to $N$ induced by application of higher electric field has been found and explained. A transformation of the structure of polar nematic phases at the application of electric field has also been investigated by Monte Carlo simulations and experimentally by observation of polarizing optical microscope images. In particular, it has been realized that, at planar anchoring, $N_{AF}$ in the presence of a moderate out-of-plane electric field exhibits twofold splay modulation: antiferroelectric in the plane of the substrate and ferroelectric in the plane normal to the substrate. Several additional subtransitions related to fitting the confined geometry of the cell by the structure of polar phases were detected.

We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation function. The algorithm is based on explicitly storing the pseudorandom numbers used to create the randomized displacements in computer simulations and subtracting them from the simulated trajectories. The resulting correlation function of the reduced motion is connected to the target correlation function up to a cross-correlation term. Using analytical theory and computer simulations, we demonstrate that the cross-correlation term can be neglected in all three systems studied in this paper. We further expand the algorithm to Monte Carlo simulations and analyze the performance of the algorithm and rationalize that it works particularly well for unbounded, weakly interacting systems in which the precision of the mean-square displacement can be improved by orders of magnitude.

We study the spectrum of a system of coupled disordered harmonic oscillators in the thermodynamic limit. This Euclidean random matrix ensemble has been suggested as a model for the low temperature vibrational properties of glass. Exact numerical diagonalization is performed in three and two spatial dimensions, which is accompanied by a detailed finite size analysis. It reveals a low-frequency regime of sound waves that are damped by Rayleigh scattering. At large frequencies localized modes exist. In between, the central peak in the vibrational density of states is well described by Wigner's semicircle law for not too large disorder, as is expected for simple random matrix systems. We compare our results with predictions from two recent self-consistent field theories.

The speed of an exhaustive search can be measured by a cover time, which is defined as the time it takes a random searcher to visit every state in some target set. Cover times have been studied in both the physics and probability literatures, with most prior works focusing on a single searcher. In this paper, we prove an explicit formula for all the moments of the cover time for many searchers on an arbitrary discrete network. Our results show that such cover times depend only on properties of the network along the shortest paths to the most distant parts of the target. This mere local dependence contrasts with the well-known result that cover times for single searchers depend on global properties of the network. We illustrate our rigorous results by stochastic simulations.

Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph robustness is a problem of major research interest. In the literature the robustness of hypergraphs so far only has been treated adopting factor-graph percolation, which describes well higher-order interactions which remain functional even after the removal of one of more of their nodes. This approach, however, fall short to describe situations in which higher-order interactions fail when any one of their nodes is removed, this latter scenario applying, for instance, to supply chains, catalytic networks, protein-interaction networks, networks of chemical reactions, etc. Here we show that in these cases the correct process to investigate is hypergraph percolation, with is distinct from factor graph percolation. We build a message-passing theory of hypergraph percolation, and we investigate its critical behavior using generating function formalism supported by Monte Carlo simulations on random graph and real data. Notably, we show that the node percolation threshold on hypergraphs exceeds node percolation threshold on factor graphs. Furthermore we show that differently from what happens in ordinary graphs, on hypergraphs the node percolation threshold and hyperedge percolation threshold do not coincide, with the node percolation threshold exceeding the hyperedge percolation threshold. These results demonstrate that any fat-tailed cardinality distribution of hyperedges cannot lead to the hyper-resilience phenomenon in hypergraphs in contrast to their factor graphs, where the divergent second moment of a cardinality distribution guarantees zero percolation threshold.

Hypergraphs are higher-order networks that capture the interactions between two or more nodes. Hypergraphs can always be represented by factor graphs, i.e., bipartite networks between nodes and factor nodes (representing groups of nodes). Despite this universal representation, here we reveal that $k$-core percolation on hypergraphs can be significantly distinct from $k$-core percolation on factor graphs. We formulate the theory of hypergraph $k$-core percolation based on the assumption that a hyperedge can be intact only if all its nodes are intact. This scenario applies, for instance, to supply chains where the production of a product requires all raw materials and all processing steps; in biology it applies to protein-interaction networks where protein complexes can function only if all the proteins are present; and it applies as well to chemical reaction networks where a chemical reaction can take place only when all the reactants are present. Formulating a message-passing theory for hypergraph $k$-core percolation, and combining it with the theory of critical phenomena on networks, we demonstrate sharp differences with previously studied factor graph $k$-core percolation processes where it is allowed for hyperedges to have one or more damaged nodes and still be intact. To solve the dichotomy between $k$-core percolation on hypegraphs and on factor graphs, we define a set of pruning processes that act either exclusively on nodes or exclusively on hyperedges and depend on their second-neighborhood connectivity. We show that the resulting second-neighbor $k$-core percolation problems are significantly distinct from each other. Moreover we reveal that although these processes remain distinct from factor graphs $k$-core processes, when the pruning process acts exclusively on hyperedges the phase diagram is reduced to the one of factor graph $k$-cores.

We simulate a two-dimensional array of droplets being compressed between two walls. The droplets are adhesive due to an attractive depletion force. As one wall moves toward the other, the droplet array is compressed and eventually induced to rearrange. The rearrangement occurs via a fracture, where depletion bonds are quickly broken between a subset of droplets. For monodisperse, hexagonally ordered droplet arrays, this fracture is preceded by a maximum force exerted on the walls, which drops rapidly after the fracture occurs. In small droplet arrays a fracture is a single well-defined event, but for larger droplet arrays, competing fractures can be observed. These are fractures nucleated nearly simultaneously in different locations. Finally, we also study the compression of bidisperse droplet arrays. The addition of a second droplet size further disrupts fracture events, showing differences between ideal crystalline arrays, crystalline arrays with a small number of defects, and fully amorphous arrays. These results are in good agreement with previously published experiments.

Collective biological systems display power laws for macroscopic quantities and are fertile probing grounds for statistical physics. Besides power laws, natural insect swarms present strong scale-free correlations, suggesting closeness to phase transitions. Swarms exhibit imperfect dynamic scaling: their dynamical correlation functions collapse into single curves when written as functions of the scaled time $t{\xi }^{-z}$ ($\xi$: correlation length, $z$: dynamic exponent), but only for short times. Triggered by markers, natural swarms are not invariant under space translations. Measured static and dynamic critical exponents differ from those of equilibrium and many nonequilibrium phase transitions. Here we show the following: (i) The recently discovered scale-free-chaos phase transition of the harmonically confined Vicsek model has a novel extended critical region for $N$ (finite) insects that contains several critical lines. (ii) As alignment noise vanishes, there are power laws connecting critical confinement and noise that allow calculating static critical exponents for fixed $N$. These power laws imply that the unmeasurable confinement strength is proportional to the perception range measured in natural swarms. (iii) Observations of natural swarms occur at different times and under different atmospheric conditions, which we mimic by considering mixtures of data on different critical lines and $N$. Unlike results of other theoretical approaches, our numerical simulations reproduce the previously described features of natural swarms and yield static and dynamic critical exponents that agree with observations.

The scaling behavior of the excited energy states of the directed polymer in random media is analyzed numerically. We find that the spatial correlations of polymer energies scale as $\sim k^{-\delta }$ for small enough wave numbers $k$ with a nontrivial exponent $\delta \approx 1.3$. The equivalence between the stochastic-field equation that describes the partition function of the directed polymer and that governing the time evolution of infinitesimal perturbations in space-time chaos is exploited to connect this exponent $\delta$ with the spatial correlations of the Lyapunov vectors reported in the literature. The relevance of our results for other problems involving optimization in random systems is discussed.

The expected utility hypothesis is a popular concept in economics that is useful for making decisions when the payoff is uncertain. In this paper, we investigate the implications of a fluctuation theorem in the theory of expected utility. In particular, we wonder whether entropy could serve as a guideline for gambling. We prove the existence of a bound involving the certainty equivalent which depends on the entropy produced. Then, we examine the dependence of the certainty equivalent on the entropy by looking at specific situations, in particular, the work extraction from a nonequilibrium initial state.

The statistical properties of turbulent flows are fundamentally different from those of systems at equilibrium due to the presence of an energy flux from the scales of injection to those where energy is dissipated by the viscous forces: a scenario dubbed “direct energy cascade.” From a statistical mechanics point of view, the cascade picture prevents the existence of detailed balance, which holds at equilibrium, e.g., in the inviscid and unforced case. Here, we aim at characterizing the nonequilibrium properties of turbulent cascades in a shell model of turbulence by studying an asymmetric time-correlation function and the relaxation behavior of an energy perturbation, measured at scales smaller or larger than the perturbed one. We contrast the behavior of these two observables in both nonequilibrium (forced and dissipated) and equilibrium (inviscid and unforced) cases. Finally, we show that equilibrium and nonequilibrium physics coexist in the same system, namely, at scales larger and smaller, respectively, of the forcing scale.

The random-magnetic-field classical Heisenberg model is solved in spatial dimensions $d\ge 2$ using the recently developed Fourier-Legendre renormalization-group theory for $4\pi$ steradians continuously orientable spins, with renormalization-group flows of 12 500 variables. The random-magnetic-field Heisenberg model is exactly solved in 10 hierarchical models, for $d=2,2.26,2.46,2.58,2.63,2.77,2.89,3$. For nonzero random fields, ferromagnetic order is seen for $d>2$. This ordering, at $d=2.46,2.58,2.63,2.77,2.89,3$, shows reentrance as a function of temperature.

Supercooled liquids show a drastic slowdown in the dynamics with decreasing temperature, while their structure remains similar to that of normal liquids. In this paper, the structural features in a quantum supercooled liquid are explored in terms of cages defined using the Voronoi polyhedra and characterized in terms of their volumes and geometries. The cage volume fluctuations are sensitive to the quantum effects, and decrease as the glass transition is approached by varying the quantumness. This is in contrast to the classical case where the volumes are insensitive to temperature variations as one approaches the transition. The cage geometry becomes more spherical upon increasing quantumness from zero, pushing the system closer to the glass transition. The cage geometry is found to be significantly correlated with asymmetry in the position uncertainty of the caged particle in the strongly quantum regime.

Networks with stochastic variables described by heavy-tailed lognormal distribution are ubiquitous in nature, and hence they deserve an exact information-theoretic characterization. We derive analytical formulas for mutual information between elements of different networks with correlated lognormally distributed activities. In a special case, we find an explicit expression for mutual information between neurons when neural activities and synaptic weights are lognormally distributed, as suggested by experimental data. Comparison of this expression with the case when these two variables have short tails reveals that mutual information with heavy tails for neurons and synapses is generally larger and can diverge for some finite variances in presynaptic firing rates and synaptic weights. This result suggests that evolution might prefer brains with heterogeneous dynamics to optimize information processing.

We study the nature of phase transitions in a self-gravitating classical gas in the presence of a central body. The central body can mimic a black hole at the center of a galaxy or a rocky core (protoplanet) in the context of planetary formation. In the chemotaxis of bacterial populations, sharing formal analogies with self-gravitating systems, the central body can be a supply of “food” that attracts the bacteria (chemoattractant). We consider both microcanonical (fixed energy) and canonical (fixed temperature) descriptions and study the inequivalence of statistical ensembles. At high energies (respectively, high temperatures), the system is in a “gaseous” phase and at low energies (respectively, low temperatures) it is in a condensed phase with a “cusp-halo” structure, where the cusp corresponds to the rapid increase of the density of the gas at the contact with the central body. For a fixed density ${\rho }_{*}$ of the central body, we show the existence of two critical points in the phase diagram, one in each ensemble, depending on the core radius $R_{*}$: for small radii $R_{*}<R_{*}^{\mathrm{MCP}}$, there exist both microcanonical and canonical phase transitions (that are zeroth and first order); for intermediate radii $R_{*}^{\mathrm{MCP}}<R_{*}<R_{*}^{\mathrm{CCP}}$, only canonical phase transitions are present; and for large radii $R_{*}>R_{*}^{\mathrm{CCP}}$, there is no phase transition at all. We study how the nature of these phase transitions changes as a function of the dimension of space. We also discuss the analogies and the differences with phase transitions in the self-gravitating Fermi gas [P. H. Chavanis, Phys. Rev. E 65, 056123 (2002)].