We show that models of opinion formation and dissemination in a community of individuals can be framed within stochastic thermodynamics from which we can build a nonequilibrium thermodynamics of opinion dynamics. This is accomplished by decomposing the original transition rate that defines an opinion model into two or more transition rates, each representing the contact with heat reservoirs at different temperatures, and postulating an energy function. As the temperatures are distinct, heat fluxes are present even at the stationary state and linked to the production of entropy, the fundamental quantity that characterizes nonequilibrium states. We apply the present framework to a generic-vote model including the majority-vote model in a square lattice and in a cubic lattice. The fluxes and the rate of entropy production are calculated by numerical simulation and by the use of a pair approximation.

We study the phase diagram of a lattice gas of $2\times 2\times 1$ hard plates on the three-dimensional cubic lattice. Each plate covers an elementary plaquette of the cubic lattice, with the constraint that a site can belong to utmost one plate. We focus on the isotropic system, with equal fugacities for the three orientations of plates. We show, using grand canonical Monte Carlo simulations, that the system undergoes two phase transitions when the density of plates is increased: the first from a disordered fluid phase to a layered phase, and the second from the layered phase to a sublattice-ordered phase. In the layered phase, the system breaks up into disjoint slabs of thickness two along one spontaneously chosen Cartesian direction, corresponding to a twofold ($Z_2$) symmetry breaking of translation symmetry along the layering direction. Plates with normals perpendicular to this layering direction are preferentially contained entirely within these slabs, while plates straddling two adjacent slabs have a lower density, thus breaking the symmetry between the three types of plates. We show that the slabs exhibit two-dimensional power-law columnar order even in the presence of a nonzero density of vacancies. In contrast, interslab correlations of the two-dimensional columnar order parameter decay exponentially with the separation between the slabs. In the sublattice-ordered phase, there is twofold symmetry breaking of lattice translation symmetry along all three Cartesian directions. We present numerical evidence that the disordered to layered transition is continuous and consistent with universality class of the three-dimensional $O\left(3\right)$ model with cubic anisotropy, while the layered to sublattice transition is first-order in nature.

We obtain the phase diagram of fully packed hard plates on the cubic lattice. Each plate covers an elementary plaquette of the cubic lattice and occupies its four vertices, with each vertex of the cubic lattice occupied by exactly one such plate. We consider the general case with fugacities $s_{\mu }$ for “$\mu$ plates,” whose normal is the $\mu$ direction ($\mu =x,y,z$). At and close to the isotropic point, we find, consistent with previous work, a phase with long-range sublattice order. When two of the fugacities $s_{{\mu }_1}$ and $s_{{\mu }_2}$ are comparable, and the third fugacity $s_{{\mu }_3}$ is much smaller, we find a spontaneously layered phase. In this phase, the system breaks up into disjoint slabs of width two stacked along the ${\mu }_3$ axis. ${\mu }_1$ and ${\mu }_2$ plates are preferentially contained entirely within these slabs, while plates straddling two successive slabs have a lower density. This corresponds to a twofold breaking of translation symmetry along the ${\mu }_3$ axis. In the opposite limit, with ${\mu }_3\gg {\mu }_1\sim {\mu }_2$, we find a phase with long-range columnar order, corresponding to simultaneous twofold symmetry breaking of lattice translation symmetry in directions ${\mu }_1$ and ${\mu }_2$. The spontaneously layered phases display critical behavior, with power-law decay of correlations in the ${\mu }_1$ and ${\mu }_2$ directions when the slabs are stacked in the ${\mu }_3$ direction, and represent examples of “floating phases” discussed earlier in the context of coupled Luttinger liquids and quasi-two-dimensional classical systems. We ascribe this remarkable behavior to the constrained motion of defects in this phase, and we sketch a coarse-grained effective field theoretical understanding of the stability of power-law order in this unusual three-dimensional floating phase.

Non-Hermitian two-site dimers serve as minimal models in which to explore the interplay of gain and loss in dynamical systems. In this paper, we experimentally and theoretically investigate the dynamics of non-Hermitian dimer models with nonreciprocal hoppings between the two sites. We investigate two types of non-Hermitian couplings; one is when asymmetric hoppings are externally introduced, and the other is when the nonreciprocal hoppings depend on the population imbalance between the two sites, thus introducing the non-Hermiticity in a dynamical manner. We engineer the models in our synthetic mechanical setup comprised of two classical harmonic oscillators coupled by measurement-based feedback. For fixed nonreciprocal hoppings, we observe that, when the strength of these hoppings is increased, there is an expected transition from a $\mathcal{PT}$-symmetric regime, where oscillations in the population are stable and bounded, to a $\mathcal{PT}$-broken regime, where the oscillations are unstable and the population grows/decays exponentially. However, when the non-Hermiticity is dynamically introduced, we also find a third intermediate regime in which these two behaviors coexist, meaning that we can tune from stable to unstable population dynamics by simply changing the initial phase difference between the two sites. As we explain, this behavior can be understood by theoretically exploring the emergent fixed points of a related dimer model in which the nonreciprocal hoppings depend on the normalized population imbalance. Our study opens the way for the future exploration of non-Hermitian dynamics and exotic lattice models in synthetic mechanical networks.

We consider conformation of a chain consisting of beads connected by stiff springs, where the conformation is determined by the bending angles between the consecutive two springs. Stability of a conformation is determined intrinsically by a potential energy function depending on the bending angles. However, effective forces induced by excited springs can change the stability, and a conformation can stay around a local maximum or a saddle of the bending potential. A stabilized conformation was named the dynamically induced conformation in a previous work on a three-body system [Y. Y. Yamaguchi et al., Phys. Rev. E 105, 064201 (2022)]. A remarkable fact is that the stabilization by the spring motion depends on the excited normal modes, which depend on a conformation. We extend analyses of the dynamically induced conformation in many-body chainlike bead-spring systems. Simple rules are that the lowest-eigenfrequency mode contributes to the stabilization and that the higher the eigenfrequency is, the more the destabilization emerges. We verify theoretical predictions by performing numerical simulations.

Dynamics of the driven Frenkel-Kontorova model with asymmetric deformable substrate potential is examined by analyzing response function, the largest Lyapunov exponent, and Poincaré sections for two neighboring particles. The obtained results show that the largest Lyapunov exponent, besides being used for investigating integral quantities, can be used for detecting microchanges in chain configuration of both damped Frenkel-Kontorova model with inertial term and its strictly overdamped limit. Slight changes in relative positions of the particles are registered through jumps of the largest Lyapunov exponent in the pinning regime. The occurrence of such jumps is highly dependent on type of commensurate structure and deformation of substrate potential. The obtained results also show that the minimal force required to initiate collective motion of the chain is not dependent on the number of Lyapunov exponent jumps in the pinning regime. These jumps are also registered in the sliding regime, where they are a consequence of a more complex structure of largest Lyapunov exponent on the step.

Loop extrusion by motor proteins mediates the attractive interactions in chromatin on the length scale of megabases, providing the polymer with a well-defined structure and at the same time determining its dynamics. The mean-square displacement of chromatin loci varies from a Rouse-like scaling to a more constrained subdiffusion, depending on cell type, genomic region, and time scale. With a simple polymeric model, we show that such a Rouse-like dynamics occurs when the parameters of the model are chosen so that contacts are local along the chain, while in the presence of nonlocal contacts we observe subdiffusion at short time scales with exponents smaller than 0.5. Such exponents are independent of the detailed choice of the parameters and build a master curve that depends only on the mean locality of the resulting contacts. We compare the loop-extrusion model with a polymeric model with static links, showing that also in this case only the presence of nonlocal contacts can produce low-exponent subdiffusion. We interpret these results in terms of a simple analytical model.

At the cellular level, all biological function relies on enzymes to provide catalytic acceleration of essential biochemical processes driving cellular metabolism. The enzyme is presumed to lower the activation energy barrier separating reactants from products, but the precise mechanism remains unresolved. Here we examine the temperature dependence of the enzyme-catalyzed dissociation of $p\text{-nitrophenyl-}\alpha \text{-D-glucopyranoside}$ ($p\mathrm{NPG}$), a chromogenic analog for maltose, isomaltose, and sucrose disaccharide sugars, into $p$-nitrophenol ($p\mathrm{NP}$) and glucose (monosaccharide). The enzymes of interest are the wild type and mutant forms of glucosidase MalL produced by the probiotic bacterium Bacillus subtilis. The per-enzyme production rates $k\left(T\right)$ for the $p\mathrm{NPG}\to$ glucose reaction all show a characteristic temperature profile with an Arrhenius-like (approximately exponential) slow acceleration at low temperatures, rising through a point of inflexion to reach a maximum, then turning over to decline steeply towards zero production at high temperatures. This asymmetric profile is found to be well fitted by convolving an exponential growth function $f\left(T\right)$ with a Gaussian temperature distribution $g\left(T\right)$ to produce an exponentially modified Gaussian function $h\left(T\right)$. To give a physical interpretation of the convolution components, we make the temperature mapping $\mathrm{\Theta }\equiv T_{\text{ref}}-T$ where $T_{\text{ref}}$ marks the temperature at which a given mutant becomes fully denatured (unfolded) and therefore inactive, then convert the convolution components to probability density functions which obey the convolution theorem of statistics. Working in $\mathrm{\Theta }$ space, we identify $f\left(\mathrm{\Theta }\right)$ as the density function for an Arrhenius-like transition from ground-state A to metastable-state B, and $g\left(\mathrm{\Theta }\right)$ as the Gaussian distribution of offset-temperature fluctuations for the metastable state. By mapping the standard thermodynamic relations for temperature and energy fluctuations to the enzyme frame of reference, we are able to derive an expression for the lifetime for the metastable B state. For the 15 enzyme experiments, we obtain a mean value $\langle \mathrm{\Delta }t\rangle \gtrsim (29.0\pm 1.3)\times {10}^{-15}\mathrm{s}$, in remarkably good agreement with the $\sim 30$-fs estimate for the period of glycosidic bond oscillations extracted from published infrared spectroscopy. We suggest that the metastable B state provides a low-energy target that has the effect of lowering the activation energy barrier by presenting an alternative axis for the reaction coordinate.

We investigate the synchronization of active rotors. A rotor is composed of a free-rotating arm with a particle that releases a surface-active chemical compound. It exhibits self-rotation due to the surface tension gradient originating from the concentration field of the surface-active compound released from the rotor. In a system with two active rotors, they should interact through the concentration field. Thus, the interaction between them does not depend only on the instantaneous positions, but also on the dynamics of the concentration field. By numerical simulations, we show that in-phase and antiphase synchronizations occur depending on the distance between the two rotors. The stability of the synchronization mode is analyzed based on phase reduction theorem through the calculation of the concentration field in the co-rotating frame with the active rotor. We also confirm that the numerical results meet the prediction by theoretical analyses.

The buckling instabilities of core-shell systems, comprising an interior elastic sphere, attached to an exterior shell, have been proposed to underlie myriad biological morphologies. To fully discuss such systems, however, it is important to properly understand the elasticity of the spherical core. Here, by exploiting well-known properties of the solid harmonics, we present a simple, direct method for solving the linear elastic problem of spheres and spherical voids with surface deformations, described by a real spherical harmonic. We calculate the corresponding bulk elastic energies, providing closed-form expressions for any values of the spherical harmonic degree $\left(l\right)$, Poisson ratio, and shear modulus. We find that the elastic energies are independent of the spherical harmonic index $\left(m\right)$. Using these results, we revisit the buckling instability experienced by a core-shell system comprising an elastic sphere, attached within a membrane of fixed area, that occurs when the area of the membrane sufficiently exceeds the area of the unstrained sphere [C. Fogle et al., Phys. Rev. E 88, 052404 (2013)]. We determine the phase diagram of the core-shell sphere's shape, specifying what value of $l$ is realized as a function of the area mismatch and the core-shell elasticity. We also determine the shape phase diagram for a spherical void bounded by a fixed-area membrane.

The three-dimensional reversible Navier-Stokes (RNS) equations are a modification of the dissipative Navier-Stokes (NS) equations, first introduced by Gallavotti [Phys. Lett. A 223, 91 (1996)], in which the energy or the enstrophy is kept constant by adjusting the viscosity over time. Spectral direct numerical simulations of this model were performed by Shukla et al. [Phys. Rev. E 100, 043104 (2019)] and Margazoglou et al. [Phys. Rev. E 105, 065110 (2022)]. Here we consider a linear, forced reversible system obtained by projecting RNS equations on a log lattice rather than on a linearly spaced grid in Fourier space, as is done in regular spectral numerical simulations. We perform numerical simulations of the system at extremely large resolutions, allowing us to explore regimes of parameters that were out of reach of the direct numerical simulations of Shukla et al. Using the nondimensionalized forcing as a control parameter, and the square root of enstrophy as the order parameter, we confirm the existence of a second-order phase transition well described by a mean-field Landau theory. The log-lattice projection allows us to probe the impact of the resolution, highlighting an imperfect transition at small resolutions with exponents differing from the mean-field predictions. Our findings are in qualitative agreement with predictions of a 1D nonlinear diffusive model, the reversible Leith model of turbulence. We then compare the statistics of the solutions of RNS and NS, in order to shed light on an adaptation of the Gallavotti conjecture, in which there is equivalence of statistics between the reversible and irreversible models, to the case where our reversible model conserves either the enstrophy or the energy. We deduce the conditions in which the two are equivalent. Our results support the validity of the conjecture and represent an instance of nonequilibrium system where ensemble equivalence holds for mean quantities.

We revisit the problem of heavy particles suspended in homogeneous box turbulence flow subjected to rotation along the vertical axis, which introduces anisotropy along the vertical and horizontal planes. We investigate the effects of the emergent structures due to rotation, on the spatial distribution and temporal statistics of the particles. The distribution of particles in the flow are studied using the joint probability distribution function (JPDFs) of the second and third principle invariants of the velocity gradient tensor, $Q$ and $R$. At high rotation rates, the JPDFs of Lagrangian $Q\text{−}R$ plots show remarkable deviations from the well-known teardrop shape. The cumulative probability distribution functions for times during which a particle remains in vortical or straining regions show exponentially decaying tails except for the deviations at the highest rotation rate. The average residence times of the particles in vortical and straining regions are also affected considerably due to the addition of rotation. Furthermore, we compute the temporal velocity autocorrelation and connect it to the Lagrangian anisotropy in presence of rotation. The spatial and temporal statistics of the particles are determined by a complex competition between the rotation rate and inertia of the particle.

In this paper, the nonlinear behavior of immiscible viscous fingering in a circular Hele-Shaw cell under the action of different time-dependent injection flow rate schemes is assessed numerically. Unlike previous studies which addressed the infinite viscosity ratio (inviscid-viscous flow), the problem is tackled by paying special attention to flows with finite viscosity ratio (viscous flow) in which the viscosity of the displacing and the displaced fluids can have any arbitrary value. Systematic numerical simulations based on a complex-variable formulation of Cauchy-Green barycentric coordinates are performed at different mobility ratios and capillary numbers with a focus on the late-time fully nonlinear regime. Additionally, numerical optimization is used to obtain the optimal flow rate schedule through a second-order weakly nonlinear stability analysis in contrast to previous studies in which the optimal flow rate was obtained entirely based on linear stability analysis. It is demonstrated that, irrespective of the values of the mobility ratio and/or the capillary number, for patterns whose constant injection counterpart exhibits linear flow regime, the curvature-driven relaxation time is comparable with the operational time of the time-dependent injection flow rate controlling schemes, and most of the controlling schemes work very well and suppress the fingering phenomenon remarkably with the maximum recovery improvement of 15%. As the nonlinearity of the system increases, the schemes may still perform well, but their effectiveness is more pronounced in patterns with less nonlinearity in their constant injection counterpart than those with higher nonlinearity. As the nonlinearity increases, the curvature-driven relaxation time becomes longer than the operational time of the schemes, leading to a reduction in their effectiveness. Additionally, it is shown that employment of the second-order weakly nonlinear stability analysis to formulate the objective function does not result in any remarkable variation in the obtained optimal flow rate schedule.

Correlation functions (CFs) are universal structural descriptors; surface-surface $F_{ss}$ and surface-void $F_{sv}$ CFs are a subset containing additional information about the interface between the phases. The description of the interface between pores and solids in porous media is of particular importance and recently Ma and Torquato [Phys. Rev. E 98, 013307 (2018)] proposed an elegant way to compute these functions for a wide variety of cases. However, their “continuous” approach is not always applicable to digital experimental 2D and 3D images of porous media as obtained using x-ray tomography or scanning electron microscopy due to nonsingularities in chemical composition or local solid material's density and partial volume effects. In this paper we propose to use edge-detecting filters to compute surface CFs in the “digital” fashion directly in the images. Computed this way, surface correlation functions are the same as analytically known for Poisson disks in case the resolution of the image is adequate. Based on the multiscale image analysis we developed a $C_{0.5}$ criterion that can predict if the imaging resolution is enough to make an accurate evaluation of the surface CFs. We also showed that in cases when the input image contains all major features, but do not pass the $C_{0.5}$ criterion, it is possible with the help of image magnification to sample CFs almost similar to those obtained for high-resolution image of the same structure with high $C_{0.5}$. The computational framework as developed here is open source and available within the CorrelationFunctions.jl package developed by our group. Our “digital” approach was applied to a wide variety of real porous media images of different quality. We discuss critical aspects of surface correlation functions computations as related to different applications. The developed methodology allows applying surface CFs to describe the structure of porous materials based on their experimental images and enhance stochastic reconstructions or super-resolution procedures, or serve as an efficient metrics in machine learning applications due to computationally effective GPU implementation.

An analytical expression for the diffusion coefficient $D$ of a free Brownian particle with velocity-dependent damping $\gamma \left(v\right)$ is derived from the Green-Kubo formula. A special case of damping that decreases monotonically with velocity is considered. At high temperature $T$, the diffusion coefficient is found to exhibit two scaling types: (i) for a power-law decrease of damping with the particle's kinetic energy, $\gamma \left(v\right)\propto 1/v^{2\alpha }$, it scales as $D\propto T^{\alpha +1}$; (ii) for a Gaussian function $\gamma \left(v\right)$, it diverges at temperatures above a critical value $T_c$ and behaves as $D\propto 1/\sqrt{T_c-T}$ at $T$ slightly below $T_c$. At $T>T_c$, the particle trajectory contains long flight events, which are not observed at $T<T_c$ in case (ii) and at all temperatures in case (i).

We demonstrate that several nonvariational continuum models commonly used to describe active matter as well as other active systems exhibit nongeneric behavior: each model supports asymmetric but stationary localized states even in the absence of pinning at heterogeneities. Moreover, such states only begin to drift following a drift-transcritical bifurcation as the activity increases. Asymmetric stationary states should only exist in variational systems, i.e., in models with gradient structure. In other words, such states are expected in passive systems, but not in active systems where the gradient structure of the model is broken by activity. We identify a “spurious” gradient dynamics structure of these models that is responsible for this nongeneric behavior, and determine the types of additional terms that render the models generic, i.e., with asymmetric states that appear via drift-pitchfork bifurcations and are generically moving. We provide detailed illustrations of our results using numerical continuation of resting and steadily drifting states in both generic and nongeneric cases.

The effect of wing shape on a forward-flying butterfly via decoupled factors of the wing-swept angle and the aspect ratio (AR) was investigated numerically. The wing-shape effect is a major concern in the design of a microaerial vehicle (MAV). In nature, the wing of a butterfly consists of partially overlapping forewing and hindwing; when the forewing sweeps forward or backward relative to the hindwing, the wing-swept angle and the AR of the entire wing simultaneously change. The effects of the wing-swept angle and AR on aerodynamics are coupled. To decouple their effects, we established wing-shape models with varied combinations of the wing-swept angle and AR based on the experimental measurement of two butterfly species (Papilio polytes and Kallima inachus) and developed a numerical simulation for analysis. In each model, the forewing and hindwing overlapped partially, constructing a single wing. Across the models, the wing-swept angle and AR of these single wings varied sequentially. The results show that, through our models, the effects of the wing-swept angle and AR were decoupled; both have distinct flow mechanisms and aerodynamic force trends and are consistent in the two butterfly species. For a fixed AR, a backward-swept wing increases lift and drag because of the enhanced attachment of the leading-edge vortex with increased strength of the wingtip vortex and the spanwise flow. For a fixed wing-swept angle, a small AR wing increases lift and decreases drag because of the large region of low pressure downstream and the wake-capture effect. Coupling these effects, the largest lift-to-drag ratio occurs for a forward-swept wing with the smallest AR. These results indicate that, in a flapping forward flight, sweeping a forewing forward relative to a hindwing is suitable for cruising. The flow mechanisms and decoupled and coupled effects of the wing-swept angle and the AR presented in this paper provide insight into the flight of a butterfly and the design of a MAV.

Electric field-induced flows involving multiple fluid components with a range of different electrical properties are described by the coupled Taylor-Melcher leaky-dielectric model. We present a lattice Boltzmann (LB)-finite difference (FD) method-based hybrid framework to solve the complete Taylor-Melcher leaky-dielectric model considering the nonlinear surface charge convection effects. Unlike the existing LB-based models, we treat the interfacial discontinuities using direction-specific continuous gradients, which prevents the miscalculation arising due to volumetric gradients without directional derivatives, simultaneously maintaining the electroneutrality of the bulk. While fluid transport is recovered through the LB method using a multiple relaxation time (MRT) scheme, the FD method with a central difference scheme is applied to discretize the charge transport equation at the interface, in addition to the electric field governing equations in the bulk and at the interface. We apply the developed numerical model to study the different regimes of droplet deformation due to an external electric field. Similar to the existing analytical and other numerical models, excluding the surface charge convection (SCC) term from the charge transport equation, the present methodology has shown excellent agreement with the existing literature. In addition, the effect of SCC in each of the regimes is analyzed. With the present numerical model, we observe a strong presence of SCC in the oblate deformation regime, contrary to the weak effect on prolate deformations. We further discuss the reason behind such differences in the magnitude of nonlinearity induced by the SCC in all the regimes of deformation.

We present a method for solving the linearized Vlasov-Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior.

Combining Monte Carlo simulations and thermodynamic integration method, we study the configurational entropy per site of straight rigid rods of length $k$ ($k$-mers) adsorbed on three-dimensional (3D) simple cubic lattices. The process is monitored by following the dependence of the lattice coverage $\theta$ on the chemical potential $\mu$ (adsorption isotherm). Then, we perform the integration of $\mu \left(\theta \right)$ over $\theta$ to calculate the configurational entropy per site of the adsorbed phase $s(k,\theta )$ as a function of the coverage. Based on the behavior of the function $s(k,\theta )$, different phase diagrams are obtained according to the $k$ values: $k\le 4$, disordered phase; $k=5,6$, disordered and layered-disordered phases; and $k\ge 7$, disordered, nematic and layered-disordered phases. In the limit of $\theta \to 1$ (full coverage), the configurational entropy per site is determined for values of $k$ ranging between 2 and 8. For $k\ge 6$, MC data coincide (within the statistical uncertainty) with recent analytical predictions [D. Dhar and R. Rajesh, Phys. Rev. E 103, 042130 (2021)] for very large rods. This finding represents the first numerical validation of the expression obtained by Dhar and Rajesh for $d$-dimensional lattices with $d>2$. In addition, for $k\ge 5$, the values of $s(k,\theta \to 1)$ for simple cubic lattices are coincident with those values reported in [P. M. Pasinetti et al., Phys. Rev. E 104, 054136 (2021)] for two-dimensional (2D) square lattices. This is consistent with the picture that at high densities and $k\ge 5$, the layered-disordered phase is formed on the lattice. Under these conditions, the system breaks to 2D layers, and the adsorbed phase becomes essentially 2D. The 2D behavior of the fully covered lattice reinforces the conjecture that the large-$k$ behavior of entropy per site is superuniversal, and holds on $d$-dimensional hypercubical lattices for all $d\ge 2$.