Physical review. E最新文献

In a transition between nonequilibrium steady states, the entropic cost associated with the maintenance of steady-state currents can be distinguished from that arising from the transition itself through the concepts of excess (housekeeping) entropy flux and adiabatic (nonadiabatic) entropy production. The thermodynamics of this transition is embodied by the Hatano-Sasa relation. In this letter, we show that for a slow transition between quantum nonequilibrium steady states the nonadiabatic entropy production is, to leading order, given by the path action with respect to a Riemannian metric in the parameter space, which can be connected to the Kubo-Mori-Bogoliubov quantum Fisher information. We then demonstrate how to obtain minimally dissipative paths by solving the associated geodesic equation and illustrate the procedure with a simple example of a three-level maser. Furthermore, by identifying the quantum Fisher information with respect to time as a metric in state space, we derive an upper bound on the excess entropy flux that holds for arbitrarily fast processes.

Since perturbations are omnipresent in physics, understanding their impact on the dynamics of quantum many-body systems is a vitally important but notoriously difficult question. On the one hand, random-matrix and typicality arguments suggest a rather simple damping in the overwhelming majority of cases, e.g., exponential damping according to Fermi's golden rule. On the other hand, counterexamples are known to exist, and it remains unclear how frequent and under which conditions such counterexamples appear. In our work, we consider the spin-1/2 XXZ chain as a paradigmatic example of a quantum many-body system and study the dynamics of the magnetization current in the easy-axis regime. Using numerical simulations based on dynamical quantum typicality, we show that the standard autocorrelation function is damped in a nontrivial way and only a modified version of this function is damped in a simple manner. Employing projection-operator techniques in addition, we demonstrate that both the nontrivial and simple damping relation can be understood on perturbative grounds. Our results are in agreement with earlier findings for the particle current in the Hubbard chain.

We consider a Brownian particle performing an overdamped motion in a power-law repulsive potential. If the potential grows with the distance faster than quadratically, the particle escapes to infinity in a finite time. We determine the average blowup time and study the probability distribution of the blowup time. In particular, we show that the long-time tail of this probability distribution decays purely exponentially, while the short-time tail exhibits an essential singularity. These qualitative features turn out to be quite universal, as they occur for all rapidly growing power-law potentials in arbitrary spatial dimensions. The quartic potential is especially tractable, and we analyze it in more detail.

This paper presents a versatile model for generating fractal complex networks that closely mirror the properties of real-world systems. By combining features of reverse renormalization and evolving network models, the proposed approach introduces several tunable parameters, offering exceptional flexibility in capturing the diverse topologies and scaling behaviors found in both natural and man-made networks. The model effectively replicates their key characteristics such as fractal dimensions, power-law degree distributions, and scale-invariant properties of hierarchically nested boxes. Unlike traditional deterministic models, it incorporates stochasticity into the network growth process, overcoming limitations like discontinuities in degree distributions and rigid size constraints. The model's applicability is demonstrated through its ability to reproduce the structural features of real-world fractal networks, including the Internet, the World Wide Web, and co-authorship networks.

We present a method for calculating the Yang-Lee partition function zeros of a translationally invariant model of lattice fermions, exemplified by the Hubbard model. The method rests on a theorem involving the usual single-electron self-energy Σ_{σ}(k[over ⃗],iω_{n}|μ) with chemical potential μ, in the imaginary time Matsubara formulation. The theorem maps the Yang-Lee zeros to a set of wave vector and spin labeled virtual energies ξ_{k[over ⃗]σ}. These, thermodynamically derived virtual energies, are solutions of the set of equations ξ_{kσ}=ɛ_{σ}(k[over ⃗])-1/2U+Σ_{σ}(k[over ⃗],iπ/β|ξ_{kσ}+1/2U-iπ/β)=0. Examples of the method in simplified situations are provided.

We consider a random walker performing a continuous-time random walk (CTRW) with a symmetric step lengths' distribution possessing a finite second moment and with a power-law waiting time distribution with finite or diverging first moment. The problem we pose concerns the distribution of the number of steps of the corresponding CTRW conditioned on the final position of the walker at some long time t. For positions within the scaling domain of the probability density function (PDF) of final displacements, the distributions of the number of steps show a considerable amount of universality, and are different in the cases when the corresponding CTRW corresponds to subdiffusion and to normal diffusion. We moreover note that the mean value of the number of steps can be obtained independently and follows from the solution of the Poisson equation whose right-hand side depends on the PDF of displacements only. This approach works not only in the scaling domain but also in the large deviation domain of the corresponding PDF, where the behavior of the mean number of steps is very sensitive to the details of the waiting time distribution beyond its power-law asymptotics.

In this study, we generalize the theory of stochastic resetting for the non-Markovian dynamics of a free Brownian particle (BP) with arbitrary damping strength and correlation time of the thermal noise. To apply this theory, we calculate the properties of the BP under thermal Ornstein-Uhlenbeck noise and compare the results with those from the Markovian dynamics case. We find that, at long times, the evolution of the distribution function toward the steady state in non-Markovian dynamics can resemble that observed in Markovian systems. In the asymptotic limit, the stationary distribution function reveals that the probability density at a given position can increase exponentially with memory time. Notably, the difference in probability density between the two cases tends to be maximal at an intermediate stage of the dynamics for a fixed memory time. Using the exact distribution function, we also calculate the variance of the position to explore a central question: How the nature of diffusion for a free particle is influenced by resetting, which can lead to a steady state. This analysis suggests that, although ballistic diffusion and memory effects may not significantly impact the long-time behavior of free Brownian motion or equilibrium in the presence of an external conservative force field, they play a crucial role in the formation of a resetting-induced localized stationary state. Additionally, we observe that the survival probability decreases exponentially at all times. Finally, we compute the mean first-passage time and uncover interesting results that provide further insights into the system's behavior.

The phenomena of senescence are widely observed during the process of cell mitosis at the cellular level. From the perspective of statistical mechanics, the senescence can be formulated by a random walk process whose dynamic and transitional properties decay as the number of transitions increases. To explore the impact of the senescence effects on anomalous diffusion, we propose a new subordinator by adding a senescence term f(s) to the classical α-stable subordinator and then establish the subordinated Langevin equation to characterize the subdiffusion with senescence effects. By taking the senescence term f(s) in the specific form of power law, we evaluate the ensemble average and time average of the mean-squared displacements and derive the Fokker-Planck equations of the propagators. The quantitative analyses reveal different diffusion regimes for the scenarios of weak senescence and strong senescence. The results show that the strong senescence effect has a damping influence and slows down the subdiffusion, while the weak senescence effect has no impact on the subdiffusion at large-time limit. The proposed Langevin equation and the quantitative analyses provide a new perspective for studying the senescence effects in anomalous diffusion phenomena.

Myosin II molecular motors slide actin filaments relatively to each other and are essential for force generation, motility, and mechanosensing in animal cells. For nonmuscle cells, evolution has resulted in three different isoforms, which have different properties concerning the motor cycle and also occur in different abundances in the cells, but their respective biological and physical roles are not fully understood. Here we use active gel theory to demonstrate the complementary roles of isoforms A and B for cell migration. We first show that our model can be derived both from coarse-graining kinetic equations and from nonequilibrium thermodynamics as the macroscopic limit of a two-component Tonks gas. We then parametrize the model and show that motile solutions exist, in which the more abundant and more dynamic isoform A is localized to the front and the stronger isoform B to the rear, in agreement with experiments. Exploring parameter space beyond the isoform parameters typical for animal cells, we also find cell oscillations in length and velocity, which might be realized for genetically engineered systems. We also describe an analytical solution for the stiff limit, which then is used to calculate a state diagram, and the effect of actin polymerization at the boundaries that leads to an imperfect pitchfork bifurcation. Our findings highlight the importance of including isoform-specific molecular details to describe whole cell behavior.

We study the evolution of two-point correlation functions of the one-dimensional Bose-Hubbard model in the semiclassical regime in the framework of truncated Wigner approximation with quantum jumps as first-order corrections. At early times, the correlation functions show strong superdiffusion with universal integer exponents determined solely by the initial conditions and completely insensitive to system parameters and chaos. Only after a long time does this regime crosse over to the normal diffusion regime which is most robust when nonintegrability is strong. For strong nonintegrability, the system ends up in a homogeneous state, while for weak nonintegrability, the oscillations and inhomogeneities persist, despite the fact that chaos is nearly always strong and only weakly depends on the nonintegrability parameter. We conclude that the superdiffusive regime is neither prethermalized nor a precursor to thermalization but an early-time phenomenon related to a special scaling symmetry of the Bose-Hubbard Hamiltonian.