Physical Review E最新文献

Singular-value statistics (SVS) has been recently presented as a random matrix theory tool able to properly characterize non-Hermitian random matrix ensembles [PRX Quantum 4, 040312 (2023)2691-339910.1103/PRXQuantum.4.040312]. Here, we perform a numerical study of the SVS of the non-Hermitian adjacency matrices A of directed random graphs, where A are members of diluted real Ginibre ensembles. We consider two models of directed random graphs: Erdös-Rényi graphs and random geometric graphs. Specifically, we focus on the singular-value-spacing ratio r and the minimum singular value λ_{min}. We show that 〈r〉 (where 〈·〉 represents ensemble average) can effectively characterize the crossover between mostly isolated vertices to almost complete graphs, while the probability density function of λ_{min} can clearly distinguish between different graph models.

Entropy production (EP) is a central quantity in nonequilibrium physics as it monitors energy dissipation, irreversibility, and free energy differences during thermodynamic transformations. Estimating EP, however, is challenging both theoretically and experimentally due to limited access to the system dynamics. For overdamped Langevin dynamics and Markov jump processes it was recently proposed that, from thermodynamic uncertainty relations (TURs), short-time cumulant currents can be used to estimate EP without knowledge of the dynamics. Yet, estimation of EP in underdamped Langevin systems remains an active challenge. To address this, we derive a modified TUR that relates the statistics of two specific currents-one cumulant current and one stochastic current-to a system's EP. These two distinct but related currents are used to constrain EP in the modified TUR. One highlight is that there always exists a family of currents such that the uncertainty relations saturate, even for long-time averages and in nonsteady-state scenarios. Another is that our method only requires limited knowledge of the dynamics-specifically, the damping coefficient to mass ratio and the diffusion constant. This uncertainty relation allows estimating EP for both overdamped and underdamped Langevin dynamics. We validate the method numerically, through applications to several underdamped systems, to underscore the flexibility in obtaining EP in nonequilibrium Langevin systems.

We study the viscoelastic relaxation dynamics of scale-free copolymer networks in the generalized Gaussian structures framework. We focus on the real and imaginary components of the complex dynamic modulus G^{*}(ω): the storage and loss moduli. Our chosen scale-free network model builds distinct types of hyperbranched copolymers by a careful tuning of the construction parameters, such as γ, which controls the node connectivity, or the minimum allowed degree K_{min} and the maximum allowed degree K_{max}. These parameters, together with the parameters that govern the monomer-type distribution, provide significative distinct behaviors. By only varying γ we change the topology of the copolymers and a local maximum in the region of high frequencies or a constant slope in the intermediate frequency region become more evident. Both K_{min} and K_{max} play an important role, especially in the region of intermediate frequency domain. The ratio σ between the friction coefficients ζ_{A} and ζ_{B} of the A and B beads gives birth to new features, such as, new quasiplateaus or new peaks along with a shift toward lower or higher frequencies depending on the ratio value. The ratio η between the number of A and B monomers influences the size of the constant slope for intermediate frequencies and it is responsible for the symmetry of the two peaks of the loss modulus.

Response to an external perturbation characterizes the fundamental nature of equilibrium and nonequilibrium systems. The response properties have been expressed by the susceptibility and the precision given by the signal to noise ratio. In this Letter, we first derive a general response equality for precision that connects susceptibilities out of equilibrium for general observables to the Fisher information measuring a sensitivity to the perturbation. In particular, this fundamental result provides kinetic equality for susceptibility (KSE), a model-independent general equality among experimentally accessible quantities such as the time derivative of observables, the dynamical activity, and fluctuation for generic nonequilibrium systems. As special limiting cases, KSE reproduces the kinetic uncertainty relation and its extensions to multiple variables. We also show an equality between the susceptibility and the observable-action covariance. Hence, KSE provides a master relation of these nonequilibrium relations.

A nonstochastic quantum engine is one that operates in a cycle of transformations in which no sources of stochasticity, such as thermal baths and projective measurements, are present and, therefore, no entropy is generated in the driven system. Defining work and heat as the energy corresponding to different types of transformations between pure states, we arrive at an expression similar to the first law of thermodynamics and prove a version of the Kelvin-Planck statement for the second law of thermodynamics. Essentially, the first law can be obtained thanks to the normalization condition of a quantum state and the second law can be obtained thanks to the orthogonalization condition between energy eigenstates. For nonstochastic engines that operate between two given energy gaps, we prove a version of Carnot's theorem. Regarding operationalization, we present a protocol that leads the system through a cycle in which heat exchange occurs by performing two quantum quenches separated by a precise time interval and involving an energy-level anticrossing. Furthermore, with this protocol it is possible to make the engine's efficiency as close to 1 as one wants; however, efficiency equal to 1 is a case prohibited by the version of the Kelvin-Planck statement that we proved. Finally, we illustrate these results in an exactly solvable single-qubit model.

We introduce an aggregation process that is based on templating, where a specified number of constituent clusters must assemble on a larger scaffold aggregate for a reaction to occur. A simple example is a dimer scaffold, upon which two monomers meet and create another dimer, while dimers and larger clusters irreversibly join at mass-independent rates. In the mean-field approximation, templating aggregation has unusual kinetics in which the monomer density m(t) and the density c(t) of all clusters heavier than monomers decay with time as c∼m^{2}∼t^{-2/3}. These strongly contrast with the corresponding behaviors in conventional aggregation, where c∼m^{1/2}∼t^{-1}. We also treat three natural extensions of templating: (a) the reaction in which L monomers meet and react on an L-mer scaffold to create two L-mers, (b) multistage scaffold reactions, and (c) templated ligation, in which clusters of all masses serve as scaffolds and binary aggregation does not occur.

There is a wide range of mathematical models that describe populations of large numbers of neurons. In this article, we focus on nonlinear noisy leaky integrate-and-fire (NNLIF) models that describe neuronal activity at the level of the membrane potential. We introduce a sequence of states, which we call pseudoequilibria, and give evidence of their defining role in the behavior of the NNLIF system when a significant synaptic delay is considered. The advantage is that these states are determined solely by the system's parameters and are derived from a sequence of firing rates that result from solving a recurrence equation. We propose a strategy to show convergence to an equilibrium for a weakly connected system with large transmission delay, based on following the sequence of pseudoequilibria. Unlike direct entropy dissipation methods, this technique allows us to see how a large delay favors convergence. We present a detailed numerical study to support our results. This study helps us understand, among other phenomena, the appearance of periodic solutions in strongly inhibitory networks.

We show that the time-resolved dynamics of an underdamped harmonic oscillator can be used to do multifunctional computation, performing distinct computations at distinct times within a single dynamical trajectory. We consider the amplitude of an oscillator whose inputs influence its frequency. The activity of the oscillator at fixed times is a nonmonotonic function of its inputs, so it can solve problems such as XOR that are not linearly separable. The activity of the oscillator at fixed input is a nonmonotonic function of time, so it is multifunctional in a temporal sense, and able to carry out distinct nonlinear computations at distinct times within the same dynamical trajectory. We show that a single oscillator, observed at different times, can act as all of the elementary logic gates and perform binary addition, the latter usually implemented in hardware using five logic gates. We show that a set of n oscillators, observed at different times, can perform an arbitrary number of analog-to-n-bit digital conversions. We also show that oscillators can be trained by gradient descent to perform distinct classification tasks at distinct times. Computing with time-dependent functionality can be done in or out of equilibrium, and suggests a way of reducing the number of parameters or devices required to do nonlinear computations.

There has been of significant interest lately in the study of electromagnetic (EM) waves interacting with magnetized plasmas. The variety of resonances and the existence of several pass and stop bands in the dispersion curve for different orientations of the magnetic field offer new mechanisms of EM wave energy absorption [1-3]. However, earlier studies have investigated only special cases of magnetized plasma geometry [e.g., RL mode (k[over ⃗]||B[over ⃗]_{ext}) or (k[over ⃗]⊥B[over ⃗]_{ext}) X,O-mode configuration]. In these specific cases, EM waves encounter specific resonances [e.g., for (θ=0) cyclotron resonances, and for (θ=π/2), hybrid resonances]. A general case of EM wave propagation is at an oblique angle with respect to the externally applied magnetic field B[over ⃗]_{ext} considered here. Furthermore, the magnetic field is chosen to be inhomogeneous such that the EM wave pulse encounters a resonance layer within the plasma medium. A 2D particle-in-cell (PIC) simulation using the OSIRIS 4.0 platform has been carried out for these studies. A significant enhancement in absorption leading to almost complete absorption of laser energy by the plasma has been observed. A detailed study characterizing the role of the external magnetic field profile, EM wave intensity, etc., has also been carried out.

We consider an isothermal self-gravitating system surrounding a central body. This model can represent a galaxy or a globular cluster harboring a central black hole. It can also represent a gaseous atmosphere surrounding a protoplanet. In three dimensions, the Boltzmann-Poisson equation must be solved numerically to obtain the density profile of the gas [Chavanis et al., Phys. Rev. E 109, 014118 (2024)10.1103/PhysRevE.109.014118]. In one and two dimensions, we show that the Boltzmann-Poisson equation can be solved analytically. We obtain explicit analytical expressions of the density profile around a central body which generalize the analytical solutions found by Camm (1950) and Ostriker (1964) in the absence of a central body. Our results also have applications for self-gravitating Brownian particles (Smoluchowski-Poisson system), for the chemotaxis of bacterial populations in biology (Keller-Segel model), and for two-dimensional point vortices in hydrodynamics (Onsager's model). In the case of bacterial populations, the central body could represent a supply of "food" that attracts the bacteria (chemoattractant). In the case of two-dimensional vortices, the central body could be a central vortex.