arXiv - PHYS - Statistical Mechanics最新文献_第10页

Scaling and universality for percolation in random networks: a unified view 随机网络中渗流的扩展性和普遍性：统一观点

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-09 DOI: arxiv-2408.05125

Lorenzo Cirigliano, Gábor Timár, Claudio Castellano

引用次数: 0

Dynamical patterns in active-passive particle mixtures with non-reciprocal interactions: Exact hydrodynamic analysis 具有非互惠相互作用的主动-被动粒子混合物的动力学模式：精确流体力学分析

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-07 DOI: arxiv-2408.03932

James Mason, Robert L. Jack, Maria Bruna

{"title":"Dynamical patterns in active-passive particle mixtures with non-reciprocal interactions: Exact hydrodynamic analysis","authors":"James Mason, Robert L. Jack, Maria Bruna","doi":"arxiv-2408.03932","DOIUrl":"https://doi.org/arxiv-2408.03932","url":null,"abstract":"The formation of dynamical patterns is one of the most striking features of\u0000non-equilibrium physical systems. Recent work has shown that such patterns\u0000arise generically from forces that violate Newton's third law, known as\u0000non-reciprocal interactions. These non-equilibrium phenomena are challenging\u0000for modern theories. Here, we introduce a model mixture of active\u0000(self-propelled) and passive (diffusive) particles with non-reciprocal\u0000effective interactions, which is amenable to exact mathematical analysis. We\u0000exploit state-of-the-art methods to derive exact hydrodynamic equations for the\u0000particle densities. We study the resulting collective behavior, including the\u0000linear stability of homogeneous states and phase coexistence in large systems.\u0000This reveals a novel phase diagram with the spinodal associated with active\u0000phase separation protruding through the associated binodal, heralding the\u0000emergence of dynamical steady states. We analyze these states in the\u0000thermodynamic limit of large system size, showing, for example, that sharp\u0000interfaces may travel at finite velocities, but traveling phase-separated\u0000states are forbidden. The model's mathematical tractability enables precise new\u0000conclusions beyond those available by numerical simulation of particle models\u0000or field theories.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes 确定性和随机反常扩散过程族中的广义自相关函数

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-06 DOI: arxiv-2408.02989

Muhammad Tayyab

{"title":"Generalized autocorrelation function in the family of deterministic and stochastic anomalous diffusion processes","authors":"Muhammad Tayyab","doi":"arxiv-2408.02989","DOIUrl":"https://doi.org/arxiv-2408.02989","url":null,"abstract":"We investigate the observables of the one-dimensional model for anomalous\u0000transport in semiconductor devices where diffusion arises from scattering at\u0000dislocations at fixed random positions, known as L'evy-Lorentz gas. Due to\u0000complex stochasticity in the system, direct investigations of such non-trivial\u0000dynamics are not possible; therefore, to gain insight into the microscopic\u0000properties, we use deterministic dynamics known as the Slicer Map and\u0000Fly-and-Die dynamics. We analytically derive the generalized position\u0000auto-correlation function of these dynamics and study the special case, the\u00003-point position correlation function. For this, we derive single\u0000parameter-dependent scaling and compare it with the numerically estimated\u00003-point position auto-correlation of the L'evy-Lorentz gas, for which the\u0000analytical expression is still an open question. Here we obtained a remarkable\u0000agreement between them, irrespective of any functional relationship with time.\u0000Moreover, we demonstrate that the position moments and the position\u0000auto-correlations of these systems scale in the same fashion, provided the\u0000times are large enough and far enough apart. Other observables, such as\u0000velocity moments and correlations, are reported to distinguish the systems.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943344","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Heat production in a stochastic system with nonlinear time-delayed feedback 具有非线性延时反馈的随机系统中的热量产生

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-06 DOI: arxiv-2408.03316

Robin A. Kopp, Sabine H. L. Klapp

{"title":"Heat production in a stochastic system with nonlinear time-delayed feedback","authors":"Robin A. Kopp, Sabine H. L. Klapp","doi":"arxiv-2408.03316","DOIUrl":"https://doi.org/arxiv-2408.03316","url":null,"abstract":"Using the framework of stochastic thermodynamics we study heat production\u0000related to the stochastic motion of a particle driven by repulsive, nonlinear,\u0000time-delayed feedback. Recently it has been shown that this type of feedback\u0000can lead to persistent motion above a threshold in parameter space [Physical\u0000Review E 107, 024611 (2023)]. Here we investigate, numerically and by\u0000analytical methods, the rate of heat production in the different regimes around\u0000the threshold to persistent motion. We find a nonzero average heat production\u0000rate, $langle dot{q}rangle$, already below the threshold, indicating the\u0000nonequilibrium character of the system even at small feedback. In this regime,\u0000we compare to analytical results for a corresponding linearized delayed system\u0000and a small-delay approximation which provides a reasonable description of\u0000$langle dot{q}rangle$ at small repulsion (or delay time). Beyond the\u0000threshold, the rate of heat production is much larger and shows a maximum as\u0000function of the delay time. In this regime, $langle dot{q}rangle$ can be\u0000approximated by that of a system subject to a constant force stemming from the\u0000long-time velocity in the deterministic limit. The distribution of dissipated\u0000heat, however, is non-Gaussian, contrary to the constant-force case.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"43 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Templating Aggregation 模板聚合

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-06 DOI: arxiv-2408.02910

P. L. Krapivsky, S. Redner

引用次数: 0

Spin glass model of in-context learning 情境学习的旋转玻璃模型

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-05 DOI: arxiv-2408.02288

Yuhao Li, Ruoran Bai, Haiping Huang

{"title":"Spin glass model of in-context learning","authors":"Yuhao Li, Ruoran Bai, Haiping Huang","doi":"arxiv-2408.02288","DOIUrl":"https://doi.org/arxiv-2408.02288","url":null,"abstract":"Large language models show a surprising in-context learning ability -- being\u0000able to use a prompt to form a prediction for a query, yet without additional\u0000training, in stark contrast to old-fashioned supervised learning. Providing a\u0000mechanistic interpretation and linking the empirical phenomenon to physics are\u0000thus challenging and remain unsolved. We study a simple yet expressive\u0000transformer with linear attention, and map this structure to a spin glass model\u0000with real-valued spins, where the couplings and fields explain the intrinsic\u0000disorder in data. The spin glass model explains how the weight parameters\u0000interact with each other during pre-training, and most importantly why an\u0000unseen function can be predicted by providing only a prompt yet without\u0000training. Our theory reveals that for single instance learning, increasing the\u0000task diversity leads to the emergence of the in-context learning, by allowing\u0000the Boltzmann distribution to converge to a unique correct solution of weight\u0000parameters. Therefore the pre-trained transformer displays a prediction power\u0000in a novel prompt setting. The proposed spin glass model thus establishes a\u0000foundation to understand the empirical success of large language models.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"44 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Thermodynamic hierarchical equations of motion and their application to Carnot engine 热力学分层运动方程及其在卡诺发动机中的应用

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-05 DOI: arxiv-2408.02249

Shoki Koyanagi, Yoshitaka Tanimura

{"title":"Thermodynamic hierarchical equations of motion and their application to Carnot engine","authors":"Shoki Koyanagi, Yoshitaka Tanimura","doi":"arxiv-2408.02249","DOIUrl":"https://doi.org/arxiv-2408.02249","url":null,"abstract":"We developed a computer code for the thermodynamic hierarchical equations of\u0000motion (T-HEOM) derived from a spin subsystem coupled to multiple Drude baths\u0000at different temperatures, which are connected to or disconnected from the\u0000subsystem as a function of time. The code can simulate the reduced dynamics of\u0000the subsystem under isothermal, isentropic, thermostatic, and entropic\u0000conditions. The thermodynamic extensive and intensive variables were calculated\u0000as physical observables, and the Gibbs and Helmholtz energies were evaluated as\u0000intensive and extensive work. The contribution of energies from the system-bath\u0000interaction was evaluated separately from the subsystem using the hierarchical\u0000elements of T-HEOM. The accuracy of the calculated results for the equilibrium\u0000distribution and two-body correlation functions of the subsystem was verified\u0000by comparison with the results obtained from the time-convolution-less Redfield\u0000equation. Non-Markovian effects in thermostatic processes were investigated by\u0000sequentially turning on and off the baths of different temperatures with\u0000different switching times and system-bath coupling. As a demonstration, a\u0000comparison was made by simulating the case where the temperature of one bath\u0000was varied over time and the case where similar temperature changes were\u0000achieved by turning on and off the baths at different temperatures. In\u0000addition, the Carnot engine was simulated under quasi-static conditions. To\u0000analyze the work done for the subsystem in the cycle, thermodynamic work\u0000diagrams were plotted as functions of intensive and extensive variables. The\u0000C++ source codes are provided as supplementary material.","PeriodicalId":501520,"journal":{"name":"arXiv - PHYS - Statistical Mechanics","volume":"60 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

What will be the Euclidean dimension of an Ising ferromagnetic cubic shell? 伊辛铁磁立方壳的欧几里得维度是多少？

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-03 DOI: arxiv-2408.01804

Ishita Tikader, Muktish Acharyya

引用次数: 0

The magnon mediated plasmon friction: a functional integral approach 磁子介导的等离子体摩擦：函数积分法

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-02 DOI: arxiv-2408.01405

Yang Wang, Ruanjing Zhang, Feiyi Liu

引用次数: 0

Real Space Renormalization Group for One-Dimensional Ising Chains 一维伊辛链的实空间重正化群

arXiv - PHYS - Statistical Mechanics Pub Date : 2024-08-02 DOI: arxiv-2408.01021

Shraddha singh, Vijay Singh

引用次数: 0