Physica A: Statistical Mechanics and its Applications最新文献

英文中文

Fundamental temperature exclusively determines the validity of superstatistics 基本温度完全决定超统计量的有效性

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.physa.2026.131302

Sergio Davis , Constanza Farías

The theory of superstatistics is a generalization of Boltzmann–Gibbs statistical mechanics that allows for temperature fluctuations and builds steady-state ensembles from the distribution of these fluctuations. Although it has been widely used for non-equilibrium steady states in complex systems, recent work has shown that superstatistics is not always applicable because certain conditions must be satisfied by the so-called fundamental inverse temperature function

β_{F}

. In this work, we present a complete set of sufficient conditions under which a steady-state model can be represented using superstatistics. We show that

β_{F}

alone, along with its derivatives, fully determines the existence and form of the underlying temperature distribution. Moreover, we provide explicit expressions for the moments and cumulants of the conditional distribution of

β

given the energy

E

, in terms of

β_{F}

, and demonstrate that superstatistical models different from the canonical require

β_{F}

to be infinitely differentiable, which excludes all polynomial cases. These results strengthen the theoretical foundations of superstatistics and offer a practical way to assess its relevance in real-world applications, such as turbulence, finance, and plasma physics.

超统计理论是玻尔兹曼-吉布斯统计力学的推广，它允许温度波动，并从这些波动的分布中建立稳态系综。虽然它已广泛用于复杂系统的非平衡稳态，但最近的工作表明，超统计量并不总是适用，因为所谓的基本逆温度函数βF必须满足某些条件。在这项工作中，我们提出了一套完整的充分条件，在这些条件下，稳态模型可以用超统计量表示。我们表明，βF及其衍生物完全决定了底层温度分布的存在和形式。此外，我们给出了β在给定能量E下的条件分布的矩量和累积量的β f的显式表达式，并证明了不同于正则的超统计模型要求β f是无限可微的，这就排除了所有多项式的情况。这些结果加强了超统计的理论基础，并提供了一种实用的方法来评估其在现实世界应用中的相关性，如湍流、金融和等离子体物理。

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引用次数: 0

Thermodynamics of data 数据热力学

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.physa.2026.131283

Borko Stosic

The recently introduced concept of generalized thermodynamics is explored here in the context of 1d, 2d and 3d data analysis, performed on samples drawn from a 3d X-ray soil sample image. Different threshold levels are used to binarize the 3d sample, wherefrom relative frequencies of binary patterns are found and then used to address finite size scaling behavior of the response functions as a function of the disorder parameter (equivalent of temperature in thermodynamics). It is found that for different threshold levels response functions for increasing sample sizes approach the thermodynamic limit from different directions, with a crossover reminiscent of a transition from open to periodic boundaries of the Ising model, implying existence of a characteristic correlation scale. It is argued here that this characteristic scale corresponds to the “natural” properties of the data, where correlations within finite size samples are neither underestimated nor overestimated. In the current context of soil this scale may be related to the so-called Representative elementary volume (REV), while in other situations this characteristic scale should be interpreted in the context of the phenomenon under study.

本文在一维、二维和三维数据分析的背景下探讨了最近引入的广义热力学概念，这些数据分析是对从三维x射线土壤样品图像中提取的样品进行的。使用不同的阈值水平对三维样本进行二值化，从中找到二进制模式的相对频率，然后用于解决响应函数作为无序参数（相当于热力学中的温度）的函数的有限尺寸缩放行为。研究发现，对于不同的阈值水平，增加样本量的响应函数从不同的方向接近热力学极限，其交叉让人想起从Ising模型的开放边界到周期边界的过渡，这意味着存在特征相关标度。本文认为，这种特征尺度与数据的“自然”属性相对应，在有限大小的样本中，相关性既不会被低估，也不会被高估。在土壤的当前背景下，这个尺度可能与所谓的代表性基本体积（REV）有关，而在其他情况下，这个特征尺度应该在所研究的现象的背景下解释。

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引用次数: 0

Can bounded environmental fluctuations shield species from extinction? Insights from a non-diffusive stochastic allee growth model 有限的环境波动能保护物种免于灭绝吗？非扩散随机小巷增长模型的启示

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.physa.2026.131301

Ayan Paul , Soumalya Mukhopadhyay

Populations experiencing Allee effects are characterized by a critical density below which extinction occurs and above which persistence is possible. Classical models incorporating environmental stochasticity often predict inevitable extinction, mainly because they assume normally distributed environmental variation with unbounded effect sizes. In contrast, natural environmental fluctuations are typically bounded and non-normal. To account for this, population dynamics are analyzed using piecewise-deterministic Markov processes (PDMPs), where environmental states evolve through a finite-state Markov chain. The analysis reveals two threshold densities: populations below the lower threshold collapse deterministically, while those above the upper threshold persist. At intermediate densities, stochastic bistability emerges, with extinction and persistence occurring at complementary probabilities. Persistence fails when carrying capacities in one state fall below Allee thresholds in another, particularly when environmental change alters per-capita growth rates in non-monotonic ways, such as through increased predation or mate limitation. These findings demonstrate that incorporating realistic bounded fluctuations alters persistence predictions, with significant implications for conservation and management.

经历Allee效应的种群的特征是一个临界密度，低于该密度会发生灭绝，高于该密度则可能持续存在。包含环境随机性的经典模型经常预测不可避免的灭绝，主要是因为它们假设具有无界效应大小的正态分布的环境变化。相反，自然环境波动通常是有界的和非正态的。为了解释这一点，使用分段确定性马尔可夫过程（PDMPs）分析种群动态，其中环境状态通过有限状态马尔可夫链进化。分析揭示了两种阈值密度：低于阈值的种群确定性地崩溃，而高于阈值的种群持续存在。在中等密度下，出现随机双稳性，消灭和持续以互补的概率发生。当一个州的承载能力低于另一个州的Allee阈值时，特别是当环境变化以非单调的方式改变人均增长率时，例如通过增加捕食或配偶限制，持久性就失败了。这些发现表明，结合现实的有界波动改变了持久性预测，对保护和管理具有重要意义。

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引用次数: 0

Synchronization and chimera dynamics in fractional-order FitzHugh-Nagumo neuronal networks with fractal connectivity 具有分形连通性的分数阶FitzHugh-Nagumo神经网络的同步和嵌合动力学

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.physa.2026.131299

Yanming Liang , Yongfeng Guo , Zifei Lin , Tomasz Kapitaniak

Chimera states, which combine coherent and incoherent domains within a single network, provide a useful dynamical picture of partial synchronization in brain activity. Motivated by evidence that epileptic networks exhibit both long-range memory and multiscale modular organization, we study a fractional-order FitzHugh-Nagumo neuronal network with modular fractal connectivity. The network is arranged on a one-dimensional ring and coupled through a Cantor-type adjacency matrix constructed by Kronecker products, which allows the hierarchical depth and inter-module links to be tuned in a controlled way. We consider both globally coupled and nonlocally coupled networks and quantify the collective dynamics using the strength of incoherence, the discontinuity measure, and the average phase velocity. Numerical simulations reveal transitions from incoherence to chimera and multi-chimera states and finally to global synchronization as coupling increases. Reducing the fractional order strengthens memory and enlarges the parameter region where heterogeneous patterns persist, whereas increasing the fractional order promotes coherent states. These results clarify how fractional memory and hierarchical connectivity can jointly regulate seizure-related synchronization and provide a modeling framework for abnormal brain rhythms.

嵌合状态结合了单个网络中的相干域和非相干域，为大脑活动的部分同步提供了有用的动态图像。基于癫痫神经网络具有长时间记忆和多尺度模块化组织的证据，我们研究了一个具有模分形连通性的分数阶fitzhuh - nagumo神经网络。网络排列在一维环上，通过Kronecker积构造的cantor型邻接矩阵进行耦合，从而允许以可控的方式调整层次深度和模块间链路。我们考虑了全局耦合和非局部耦合网络，并使用非相干强度、不连续测量和平均相速度来量化集体动力学。数值模拟表明，随着耦合的增加，从非相干状态转变为嵌合体状态和多嵌合体状态，最后转变为全局同步状态。减小分数阶能增强记忆并扩大异质模式持续存在的参数区域，而增大分数阶能促进相干状态。这些结果阐明了分数记忆和层次连接如何共同调节癫痫相关的同步，并为异常脑节律提供了建模框架。

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引用次数: 0

Ultrafast Extreme Events: Empirical analysis of mechanisms and recovery in a historical perspective 超快极端事件：历史视角下的机制与恢复实证分析

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-14 DOI: 10.1016/j.physa.2026.131285

Luca Henrichs, Anton J. Heckens, Thomas Guhr

To understand the emergence of Ultrafast Extreme Events (UEEs), the influence of algorithmic trading or high–frequency traders is of major interest as they make it extremely difficult to intervene and to stabilize financial markets. In an empirical analysis, we compare various characteristics of UEEs over different years for the US stock market to assess the possible non–stationarity of the effects. We show that liquidity plays a dominant role in the emergence of UEEs and find a general pattern in their dynamics. We also empirically investigate the after–effects in view of the recovery rate. We find common patterns for different years. We explain changes in the recovery rate by varying market sentiments for the different years. Overall, our results hint at a certain degree of universal behavior.

为了理解超快极端事件（uee）的出现，算法交易或高频交易者的影响是主要的兴趣，因为它们使干预和稳定金融市场变得极其困难。在实证分析中，我们比较了美国股票市场不同年份的uee的各种特征，以评估其影响可能的非平稳性。我们表明，流动性在uee的出现中起着主导作用，并在其动态中找到了一般模式。我们还从恢复率的角度对其后效进行了实证研究。我们发现了不同年份的共同模式。我们通过不同年份不同的市场情绪来解释回收率的变化。总的来说，我们的结果暗示了某种程度上的普遍行为。

引用次数: 0

Spectral mechanism and nearly reducible transfer matrices for pseudotransitions in one-dimensional systems 一维系统中伪跃迁的谱机制和近似可约转移矩阵

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.physa.2026.131295

Onofre Rojas

While true phase transitions are forbidden in one-dimensional systems with short-range interactions, several models have recently been shown to exhibit sharp yet analytic thermodynamic anomalies that mimic thermal phase transitions. We show that this behavior arises from transfer matrices that are mathematically irreducible but possess a nearly block-diagonal structure due to the weak contribution of off-diagonal Boltzmann weights in the low-temperature regime. This results in weakly coupled competing sectors whose eigenvalue competition produces abrupt crossovers without nonanalyticity, a mechanism we term nearly block-diagonal irreducible. A key thermodynamic signature of such pseudotransitions is that the residual entropy at the interface remains bounded between the residual entropies of the competing sectors. We develop a general spectral framework to describe this behavior and apply it to two representative models: the Ising chain with internal degeneracy (Doniach model) and a hexagonal nanowire chain with mixed spin-1/2 and spin-1 components. In the first case, we derive exact expressions for the pseudo-critical temperature and residual entropy. In the second, we reduce the full 1458 × 1458 transfer matrix via symmetry decomposition and construct a low-rank effective matrix that accurately captures the crossover between quasi-ferromagnetic and quasi-core-ferromagnetic regimes. Our results demonstrate that pseudotransitions can be understood as spectral phenomena emerging from irreducible but functionally decoupled structures within the transfer matrix.

虽然在具有短程相互作用的一维系统中禁止真正的相变，但最近有几个模型显示出模仿热相变的尖锐的分析热力学异常。我们证明了这种行为是由数学上不可约的转移矩阵引起的，但由于低温状态下非对角玻尔兹曼权值的微弱贡献，转移矩阵具有近块对角结构。这导致弱耦合竞争扇区，其特征值竞争产生无非分析性的突然交叉，我们称之为近块对角不可约机制。这种伪跃迁的一个关键热力学特征是，界面上的剩余熵在竞争扇区的剩余熵之间保持有界。我们建立了一个通用的谱框架来描述这种行为，并将其应用于两个代表性模型：具有内简并的Ising链（Doniach模型）和具有混合自旋-1/2和自旋-1分量的六边形纳米线链。在第一种情况下，我们导出了伪临界温度和剩余熵的精确表达式。其次，我们通过对称分解对1458 × 1458传输矩阵进行约简，构造了一个低秩有效矩阵，准确捕获了准铁磁和准核铁磁之间的交叉。我们的研究结果表明，伪跃迁可以理解为从传递矩阵内不可约但功能解耦的结构中出现的光谱现象。

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引用次数: 0

On the paradoxical relationship between the heat equation and a traveling-wave solution 热方程与行波解的矛盾关系

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-13 DOI: 10.1016/j.physa.2026.131296

Hironari Miyoshi

We investigate the relationship between Brownian motion, which has infinite propagation speed, and a traveling-wave solution with finite propagation speed in the heat equation. First, we define a random walk associated with the Goldstein–Taylor model, a finite-speed approximation of the heat equation. We then introduce a random walk associated with the traveling-wave solutions and analyze its scaling limits, yielding three distinct stochastic processes. Finally, we conclude that the particle motion in a traveling-wave solution includes a mixture of Brownian motion and drift.

研究了热方程中具有无限传播速度的布朗运动与具有有限传播速度的行波解之间的关系。首先，我们定义了与Goldstein-Taylor模型相关的随机游走，这是热量方程的有限速度近似值。然后，我们引入了与行波解相关的随机游走，并分析了其缩放极限，得到了三个不同的随机过程。最后，我们得出结论，行波溶液中的粒子运动包括布朗运动和漂移的混合。

引用次数: 0

Productivity dispersion and allocation of labor among firms in economics 经济学中企业间的生产率分散与劳动配置

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.physa.2026.131286

Yoshi Fujiwara , Hideaki Aoyama

Inequalities are ubiquitous in economics. In this paper, we investigate productivity dispersion and the allocation of workers among different levels of productivity and output, by using a large dataset for small and medium-sized companies at a nationwide scale. Focusing on the manufacturing sector and small and medium levels of productivity, where more workers are distributed among higher levels of productivity, we first observe that the productivity dispersion can be characterized by a power-law distribution. We then have new empirical findings in a pivotal role of workers’ allocation among different levels of output as a key to understand their allocation among different levels of productivity. We also propose a stochastic process, mathematically a jump Markov process, in which workers are allocated to firms of differing output and productivity, interrupted by transitions to unemployment, where transitions are coupled with growth and shrink of firms output that relate with fluctuations of demand.

不平等在经济学中无处不在。本文利用全国范围内中小企业的大型数据集，研究了生产率分散和工人在不同生产率和产出水平之间的分配。专注于制造业和中小型生产力水平，其中更多的工人分布在更高的生产力水平，我们首先观察到生产力分散可以用幂律分布来表征。然后，我们有新的实证发现，工人在不同产出水平之间的分配是理解工人在不同生产力水平之间分配的关键。我们还提出了一个随机过程，在数学上是一个跳跃马尔可夫过程，在这个过程中，工人被分配到产出和生产率不同的公司，被向失业的过渡所打断，其中过渡与与需求波动相关的公司产出的增长和收缩相结合。

引用次数: 0

Subdiffusion supports barrier crossing: Mittag-Leffler noise autocorrelation and reactive flux formalism as evidence 亚扩散支持屏障穿越：以Mittag-Leffler噪声自相关和反应通量形式论为证据

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.physa.2026.131281

Evangelos Bakalis, Francesco Zerbetto

Rate constants govern the overcoming of potential energy barriers in chemical reactions. In the simplest approach, quasi-equilibrium in the presence of a white noise bath is advocated as the triggering mechanism. Heat baths can be tricky; around the barrier, they can retain memory, which entails non-white noise. The generalised Langevin equation is here used as the underlying model with a noise term whose autocorrelation is described by a Mittag-Leffler function of one, two, or three parameters. In the framework of reactive flux formalism, the rate constant is calculated directly as a function of the barrier height, the friction coefficient, and the parameters of the employed Mittag-Leffler function. In the strong damping limit, because of the generality of the approach, it becomes clear that noises that lead to subdiffusion promote barrier crossing as opposed to those that support superdiffusion.

速率常数控制着化学反应中势能势垒的克服。在最简单的方法中，主张在存在白噪声浴中的准平衡作为触发机制。热水浴可能很棘手；在屏障周围，他们可以保留记忆，这需要非白噪音。这里使用广义朗之万方程作为具有噪声项的基础模型，噪声项的自相关性由一个、两个或三个参数的Mittag-Leffler函数描述。在反应通量的形式框架中，速率常数直接计算为势垒高度、摩擦系数和所采用的Mittag-Leffler函数参数的函数。在强阻尼极限下，由于该方法的通用性，很明显，导致亚扩散的噪声与支持超扩散的噪声相反，促进了屏障的跨越。

引用次数: 0

Opportunity polarization: A divided world 机会极化：一个分裂的世界

IF 3.1 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Physica A: Statistical Mechanics and its Applications

Pub Date : 2026-01-12 DOI: 10.1016/j.physa.2026.131284

Yong Tao , Hualong Li

The phenomenon of escalating global inequality, where the top 1 % are amassing an ever-larger share of total wealth, has been widely documented. To shed light on this trend, we analyze two decades of household income data from the United States, China, and the United Kingdom, revealing that their income distributions can be characterized approximately by a two-class decomposition: a broad exponential distribution transitioning into a Pareto distribution in the upper-income tail. Based on this decomposition, we apply the Dragon-King test to monitor the shifts of statistical representatives of income segments between the exponential and Pareto regions, observing a significant increase in their income share upon entering the latter. This pattern is attributed to the positive correlation between earning probability and past income accumulation, intrinsic to the Pareto distribution. Conversely, within the exponential region, income growth is statistically independent of current income, reflecting more equitable opportunities. This research highlights opportunity polarization favoring certain top earners.

全球不平等加剧的现象已经被广泛记录下来，其中最富有的1% 在总财富中所占的份额越来越大。为了阐明这一趋势，我们分析了美国、中国和英国20年来的家庭收入数据，发现这些国家的收入分布大致可以用两类分解来表征：高收入尾部的广泛指数分布过渡到帕累托分布。基于这种分解，我们运用龙王检验来监测收入阶层的统计代表在指数区和帕累托区之间的变化，观察到他们的收入份额在进入后者后显着增加。这种模式归因于收入概率与过去收入积累之间的正相关关系，这是帕累托分布固有的。相反，在指数区域内，收入增长在统计上独立于当前收入，反映了更公平的机会。这项研究强调了机会极化有利于某些高收入者。

引用次数: 0

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