Pub Date : 2024-08-20DOI: 10.1088/1742-5468/ad65e4
Weisong Liu, Jun Zhang, Abdul Rahim Rasa, Weiguo Song
<bold>Abstract</bold> Avoiding collisions between pedestrians is not based solely on geometric approaches, but also involves human social conventions. Previous collision avoidance models on pedestrians often overlooked the significance of personal space and intrusion variations of intruders such as intrusion angles, intrusion extents and danger levels. The avoidance behavior of pedestrians is affected by the relative position, movement direction and distance from their initial position to the path intersection point with the intruders. To build and calibrate a pedestrian avoidance model, virtual reality and realistic experiments with dynamic and static intruders were conducted under different conditions. The critical avoidance boundary, avoidance process function and probability of avoidance side are analyzed from the experiments. Through a comparative analysis, the differences between personal and geometric space required for avoidance were identified. Moreover, an avoidance model that calculates the steering angle based on the kinematic constraints and relative position of intruders is incorporated into the social force model in this study. It successfully replicates pedestrian avoidance behavior when faced with both static and dynamic intruders, and offers a valuable tool for addressing complex pedestrian movements in highly competitive spatial environments.
{"title":"A modified social force model considering collision avoidance based on empirical studies","authors":"Weisong Liu, Jun Zhang, Abdul Rahim Rasa, Weiguo Song","doi":"10.1088/1742-5468/ad65e4","DOIUrl":"https://doi.org/10.1088/1742-5468/ad65e4","url":null,"abstract":"<title>\u0000<bold>Abstract</bold>\u0000</title>Avoiding collisions between pedestrians is not based solely on geometric approaches, but also involves human social conventions. Previous collision avoidance models on pedestrians often overlooked the significance of personal space and intrusion variations of intruders such as intrusion angles, intrusion extents and danger levels. The avoidance behavior of pedestrians is affected by the relative position, movement direction and distance from their initial position to the path intersection point with the intruders. To build and calibrate a pedestrian avoidance model, virtual reality and realistic experiments with dynamic and static intruders were conducted under different conditions. The critical avoidance boundary, avoidance process function and probability of avoidance side are analyzed from the experiments. Through a comparative analysis, the differences between personal and geometric space required for avoidance were identified. Moreover, an avoidance model that calculates the steering angle based on the kinematic constraints and relative position of intruders is incorporated into the social force model in this study. It successfully replicates pedestrian avoidance behavior when faced with both static and dynamic intruders, and offers a valuable tool for addressing complex pedestrian movements in highly competitive spatial environments.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"13 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-15DOI: 10.1088/1742-5468/ad6426
Wei Liu, Jincheng Wang, Fangfang Wang, Kai Qi, Zengru Di
In this paper, we investigate phase transitions in the majority-vote model coupled with noise layers of different structures. We examine the square lattice and random-regular networks, as well as their combinations, for both vote layers and noise layers. Our findings reveal the presence of independent third-order transitions in all cases and dependent third-order transitions when critical transitions occur. This suggests that dependent third-order transitions may serve as precursors to critical transitions in non-equilibrium systems. Furthermore, we observe that when the structure of vote layers is decentralized, the coupling between the vote layer and the noise layer leads to the absence of critical phenomena.
{"title":"The precursor of the critical transitions in majority vote model with the noise feedback from the vote layer","authors":"Wei Liu, Jincheng Wang, Fangfang Wang, Kai Qi, Zengru Di","doi":"10.1088/1742-5468/ad6426","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6426","url":null,"abstract":"In this paper, we investigate phase transitions in the majority-vote model coupled with noise layers of different structures. We examine the square lattice and random-regular networks, as well as their combinations, for both vote layers and noise layers. Our findings reveal the presence of independent third-order transitions in all cases and dependent third-order transitions when critical transitions occur. This suggests that dependent third-order transitions may serve as precursors to critical transitions in non-equilibrium systems. Furthermore, we observe that when the structure of vote layers is decentralized, the coupling between the vote layer and the noise layer leads to the absence of critical phenomena.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"18 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188528","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Sherrington–Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.
{"title":"Quenches in the Sherrington–Kirkpatrick model","authors":"Vittorio Erba, Freya Behrens, Florent Krzakala, Lenka Zdeborová","doi":"10.1088/1742-5468/ad685a","DOIUrl":"https://doi.org/10.1088/1742-5468/ad685a","url":null,"abstract":"The Sherrington–Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that locally aim to decrease energy. We analyse the energy at convergence for two distinct algorithmic classes, single-spin flip and synchronous dynamics, focusing on greedy and reluctant strategies. We provide precise numerical analysis of the finite size effects and conclude that, perhaps counter-intuitively, the reluctant algorithm is compatible with converging to the ground state energy density, while the greedy strategy is not. Inspired by the single-spin reluctant and greedy algorithms, we investigate two synchronous time algorithms, the sync-greedy and sync-reluctant algorithms. These synchronous processes can be analysed using dynamical mean field theory (DMFT), and a new backtracking version of DMFT. Notably, this is the first time the backtracking DMFT is applied to study dynamical convergence properties in fully connected disordered models. The analysis suggests that the sync-greedy algorithm can also achieve energies compatible with the ground state, and that it undergoes a dynamical phase transition.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"23 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-15DOI: 10.1088/1742-5468/ad613a
Cécile Monthus
Continuity equations associated with continuous-time Markov processes can be considered as Euclidean Schrödinger equations, where the non-Hermitian quantum Hamiltonian <inline-formula> <tex-math><?CDATA $boldsymbol{H} = {mathbf{div}}{boldsymbol{J}}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mi mathvariant="bold-italic">H</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant="bold">div</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant="bold-italic">J</mml:mi></mml:mrow></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad613aieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> is naturally factorized into the product of the divergence operator <inline-formula> <tex-math><?CDATA ${mathbf{div}}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant="bold">div</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad613aieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula> and the current operator <bold> <italic toggle="yes">J</italic> </bold>. For non-equilibrium Markov jump processes in a space of <italic toggle="yes">N</italic> configurations with <italic toggle="yes">M</italic> links and <inline-formula> <tex-math><?CDATA $C = M-(N-1)unicode{x2A7E} 1$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mo>−</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mtext>⩾</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad613aieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> independent cycles, this factorization of the <italic toggle="yes">N</italic> × <italic toggle="yes">N</italic> Hamiltonian <inline-formula> <tex-math><?CDATA ${boldsymbol{H}} = {boldsymbol{I}}^{dagger}{boldsymbol{J}}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="bold-italic">H</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant="bold-italic">I</mml:mi></mml:mrow><mml:mrow><mml:mo>†</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mi mathvariant="bold-italic">J</mml:mi></mml:mrow></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad613aieqn4.gif" xlink:type="simple"></inline-graphic> </inline-formula> involves the incidence matrix <bold> <italic toggle="yes">I</italic> </bold> and the current matrix <bold> <italic toggle="yes">J</italic> </bold> of size <italic toggle="yes">M</italic> × <italic toggle="yes">N</italic>, so that the supersymmetric partner <inline-formula> <tex-math><?CDATA ${hat{boldsymbol{H}}} = {boldsymbol{J}}{boldsymbol{I}}^{dagger}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mi mathvariant="bold-italic">H</mml:mi><mml:mo stretchy="true">^</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant="bold
与连续时间马尔可夫过程相关的连续性方程可视为欧几里得薛定谔方程，其中非赫米态量子哈密顿方程 H=divJ 自然被因子化为发散算子 div 与电流算子 J 的乘积。对于具有 M 个链接和 C=M-(N-1)⩾1 个独立循环的 N 个构型空间中的非平衡马尔可夫跃迁过程，N × N 哈密顿H=I†J 的这种因式分解涉及大小为 M × N 的入射矩阵 I 和电流矩阵 J，因此支配存在于 M 个链接上的电流动力学的超对称伙伴 H^=JI† 的大小为 M × M。为了更好地理解这两个哈密顿的频谱分解 H=I†J 和 H^=JI† 与它们的左右特征向量双正交基础之间的关系，这两个特征向量描述了向稳态的弛豫动力学和稳态电流，分析大小为 M × N 的两个矩形矩阵 I 和 J 的奇异值分解的性质以及离散亥姆霍兹分解的解释是有用的。这个关于马尔科夫跃迁过程的一般框架可以适用于由 d 维福克-普朗克方程控制的非平衡扩散过程，在此过程中，配置数 N、链接数 M 和独立循环数 C=M-(N-1) 变得无限大，而两个矩阵 I 和 J 成为作用于标量函数的一阶微分算子，从而产生矢量场。
{"title":"Markov generators as non-Hermitian supersymmetric quantum Hamiltonians: spectral properties via bi-orthogonal basis and singular value decompositions","authors":"Cécile Monthus","doi":"10.1088/1742-5468/ad613a","DOIUrl":"https://doi.org/10.1088/1742-5468/ad613a","url":null,"abstract":"Continuity equations associated with continuous-time Markov processes can be considered as Euclidean Schrödinger equations, where the non-Hermitian quantum Hamiltonian <inline-formula>\u0000<tex-math><?CDATA $boldsymbol{H} = {mathbf{div}}{boldsymbol{J}}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi mathvariant=\"bold-italic\">H</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">div</mml:mi></mml:mrow></mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">J</mml:mi></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad613aieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> is naturally factorized into the product of the divergence operator <inline-formula>\u0000<tex-math><?CDATA ${mathbf{div}}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mrow><mml:mi mathvariant=\"bold\">div</mml:mi></mml:mrow></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad613aieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and the current operator <bold>\u0000<italic toggle=\"yes\">J</italic>\u0000</bold>. For non-equilibrium Markov jump processes in a space of <italic toggle=\"yes\">N</italic> configurations with <italic toggle=\"yes\">M</italic> links and <inline-formula>\u0000<tex-math><?CDATA $C = M-(N-1)unicode{x2A7E} 1$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>C</mml:mi><mml:mo>=</mml:mo><mml:mi>M</mml:mi><mml:mo>−</mml:mo><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=\"false\">)</mml:mo><mml:mtext>⩾</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad613aieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> independent cycles, this factorization of the <italic toggle=\"yes\">N</italic> × <italic toggle=\"yes\">N</italic> Hamiltonian <inline-formula>\u0000<tex-math><?CDATA ${boldsymbol{H}} = {boldsymbol{I}}^{dagger}{boldsymbol{J}}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">H</mml:mi></mml:mrow><mml:mo>=</mml:mo><mml:msup><mml:mrow><mml:mi mathvariant=\"bold-italic\">I</mml:mi></mml:mrow><mml:mrow><mml:mo>†</mml:mo></mml:mrow></mml:msup><mml:mrow><mml:mi mathvariant=\"bold-italic\">J</mml:mi></mml:mrow></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad613aieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> involves the incidence matrix <bold>\u0000<italic toggle=\"yes\">I</italic>\u0000</bold> and the current matrix <bold>\u0000<italic toggle=\"yes\">J</italic>\u0000</bold> of size <italic toggle=\"yes\">M</italic> × <italic toggle=\"yes\">N</italic>, so that the supersymmetric partner <inline-formula>\u0000<tex-math><?CDATA ${hat{boldsymbol{H}}} = {boldsymbol{J}}{boldsymbol{I}}^{dagger}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mrow><mml:mover><mml:mi mathvariant=\"bold-italic\">H</mml:mi><mml:mo stretchy=\"true\">^</mml:mo></mml:mover></mml:mrow></mml:mrow><mml:mo>=</mml:mo><mml:mrow><mml:mi mathvariant=\"bold","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"7 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188527","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-15DOI: 10.1088/1742-5468/ad66c5
Jitendra Kethepalli, Manas Kulkarni, Anupam Kundu, Satya N Majumdar, David Mukamel, Grégory Schehr
We investigate the full counting statistics of a harmonically confined 1d short range Riesz gas consisting of <italic toggle="yes">N</italic> particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent <italic toggle="yes">k</italic> > 1 which includes the Calogero–Moser model for <italic toggle="yes">k</italic> = 2. We examine the probability distribution of the number of particles in a finite domain <inline-formula> <tex-math><?CDATA $[-W, W]$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mo>−</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>W</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad66c5ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> called number distribution, denoted by <inline-formula> <tex-math><?CDATA $mathcal{N}(W, N)$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad66c5ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>. We analyze the probability distribution of <inline-formula> <tex-math><?CDATA $mathcal{N}(W, N)$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad66c5ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula> and show that it exhibits a large deviation form for large <italic toggle="yes">N</italic> characterized by a speed <inline-formula> <tex-math><?CDATA $N^{frac{3k+2}{k+2}}$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mfrac><mml:mrow><mml:mn>3</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad66c5ieqn4.gif" xlink:type="simple"></inline-graphic> </inline-formula> and by a large deviation function (LDF) of the fraction <inline-formula> <tex-math><?CDATA $c = mathcal{N}(W, N)/N$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad66c5ieqn5.gif" xlink:type="simple"></inline-graphic> </inline-formula> of the particles inside the domain and <italic toggle="yes">W</italic>. We show that the density profiles
我们研究了由 N 个在有限温度下处于平衡状态的粒子组成的谐约束 1d 短程里兹气体的全计数统计。粒子通过指数为 k > 1 的幂律斥力相互作用相互影响，其中包括 k = 2 的卡洛吉罗-莫泽模型。我们研究的是有限域 [-W,W] 中粒子数量的概率分布，称为数量分布，用 N(W,N) 表示。我们分析了 N(W,N)的概率分布，并证明它在大 N 的情况下表现出大偏差形式，其特征是速度 N3k+2k+2 和域内粒子分数 c=N(W,N)/N 的大偏差函数 (LDF)。基于 Metropolis-Hashtings（MH）算法的蒙特卡洛模拟结果表明，我们对相应密度曲线的分析表达式与之非常吻合。我们发现，通过场论计算得到的 N(W,N)的典型波动是高斯分布的，其方差与 Nνk 成比例，νk=(2-k)/(2+k)。我们还给出了一些关于均值和方差的数值结果。此外，我们还调整了形式主义，以研究指数分布（域为半无限（-∞,W]）、线性统计（方差）、热力学压力和体积模量。
{"title":"Full counting statistics of 1d short range Riesz gases in confinement","authors":"Jitendra Kethepalli, Manas Kulkarni, Anupam Kundu, Satya N Majumdar, David Mukamel, Grégory Schehr","doi":"10.1088/1742-5468/ad66c5","DOIUrl":"https://doi.org/10.1088/1742-5468/ad66c5","url":null,"abstract":"We investigate the full counting statistics of a harmonically confined 1d short range Riesz gas consisting of <italic toggle=\"yes\">N</italic> particles in equilibrium at finite temperature. The particles interact with each other through a repulsive power-law interaction with an exponent <italic toggle=\"yes\">k</italic> > 1 which includes the Calogero–Moser model for <italic toggle=\"yes\">k</italic> = 2. We examine the probability distribution of the number of particles in a finite domain <inline-formula>\u0000<tex-math><?CDATA $[-W, W]$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mo>−</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>W</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad66c5ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> called number distribution, denoted by <inline-formula>\u0000<tex-math><?CDATA $mathcal{N}(W, N)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad66c5ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>. We analyze the probability distribution of <inline-formula>\u0000<tex-math><?CDATA $mathcal{N}(W, N)$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad66c5ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and show that it exhibits a large deviation form for large <italic toggle=\"yes\">N</italic> characterized by a speed <inline-formula>\u0000<tex-math><?CDATA $N^{frac{3k+2}{k+2}}$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi>N</mml:mi><mml:mrow><mml:mfrac><mml:mrow><mml:mn>3</mml:mn><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>k</mml:mi><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:mfrac></mml:mrow></mml:msup></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad66c5ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and by a large deviation function (LDF) of the fraction <inline-formula>\u0000<tex-math><?CDATA $c = mathcal{N}(W, N)/N$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>c</mml:mi><mml:mo>=</mml:mo><mml:mrow><mml:mi>N</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>W</mml:mi><mml:mo>,</mml:mo><mml:mi>N</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad66c5ieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> of the particles inside the domain and <italic toggle=\"yes\">W</italic>. We show that the density profiles ","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"45 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of <italic toggle="yes">L</italic> sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, <inline-formula> <tex-math><?CDATA $langle mathcal{Q}_i^2(T) rangle_c$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo fence="false" stretchy="false">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mo fence="false" stretchy="false">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad5c56ieqn1.gif" xlink:type="simple"></inline-graphic> </inline-formula> and <inline-formula> <tex-math><?CDATA $langle mathcal{Q}_{textrm{sub}}^2(l, T) rangle_c$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo fence="false" stretchy="false">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mtext>sub</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mo fence="false" stretchy="false">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad5c56ieqn2.gif" xlink:type="simple"></inline-graphic> </inline-formula>, of cumulative (time-integrated) currents up to time <italic toggle="yes">T</italic> across the <italic toggle="yes">i</italic>th bond and across a subsystem of size <italic toggle="yes">l</italic> (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large <inline-formula> <tex-math><?CDATA $L gg 1$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mi>L</mml:mi><mml:mo>≫</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad5c56ieqn3.gif" xlink:type="simple"></inline-graphic> </inline-formula>, the second cumulant <inline-formula> <tex-math><?CDATA $langle mathcal{Q}_i^2(T) rangle_c$?></tex-math> <mml:math overflow="scroll"><mml:mrow><mml:mo fence="false" stretchy="false">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy="false">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo><mml:msub><mml:mo fence="false" stretchy="false">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math> <inline-graphic xlink:href="jstatad5c56ieqn4.gif" xlink:type="simple"></inline-graphic> </inline-formula> of the cumulative current up to time <italic
我们研究了由 L 个位点组成的环上随机平均过程的几种变体中电流和质量的稳态动态波动。这些过程违反了大体的详细平衡，具有非对称的空间结构：它们的稳态不是由玻尔兹曼-吉布斯分布描述的，可能具有非零空间相关性。利用微观方法，我们分别精确计算了第 i 个键和大小为 l 的子系统（子系统中各键的总和）截至时间 T 的累积（时间积分）电流的二次累积量或方差⟨Qi2(T)⟩c 和⟨Qsub2(l,T)⟩c。我们还计算了子系统质量的（两点）动态相关函数。我们特别指出，对于大 L≫1，在初始时间 T∼O(1)时，直到时间 T 跨第 i 个键的累积电流的第二累积量⟨Qi2(T)⟩c 以⟨Qi2⟩c∼T 的线性方式增长、对于中间时间 1≪T≪L2，以⟨Qi2⟩c∼T1/2 的方式线性增长；对于长时间 T≫L2 ，以⟨Qi2⟩c∼T 的方式线性增长。当先取大子系统尺寸极限，后取大时间极限时，大小为 l 的子系统上的电流到时间 T 的标度累积量 liml→∞,T→∞⟨Qsub2(l,T)⟩c/2lT 收敛到与密度相关的粒子迁移率 χ(ρ) ；当极限相反时，它直接消失。值得注意的是，无论动力学规则如何，作为标度时间 y=DT/L2 函数的标度电流累积量 D⟨Qi2(T)⟩c/2χL≡W(y)都可以用一个通用的标度函数 W(y) 来表示，其中 D 是体扩散系数；有趣的是，中时间亚扩散增长和长时间扩散增长可以通过一个标度函数 W(y) 连接起来。电流和质量的功率谱也由各自的缩放函数精确表征。此外，我们还从微观上推导出了类似于平衡的格林-久保关系和爱因斯坦关系，它们分别将稳态电流波动与 "运行 "流动性（即对外部力场的响应）和质量波动联系起来。
{"title":"Dynamic fluctuations of current and mass in nonequilibrium mass transport processes","authors":"Animesh Hazra, Anirban Mukherjee, Punyabrata Pradhan","doi":"10.1088/1742-5468/ad5c56","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5c56","url":null,"abstract":"We study steady-state dynamic fluctuations of current and mass in several variants of random average processes on a ring of <italic toggle=\"yes\">L</italic> sites. These processes violate detailed balance in the bulk and have nontrivial spatial structures: their steady states are not described by the Boltzmann–Gibbs distribution and can have nonzero spatial correlations. Using a microscopic approach, we exactly calculate the second cumulants, or the variance, <inline-formula>\u0000<tex-math><?CDATA $langle mathcal{Q}_i^2(T) rangle_c$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:msub><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad5c56ieqn1.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> and <inline-formula>\u0000<tex-math><?CDATA $langle mathcal{Q}_{textrm{sub}}^2(l, T) rangle_c$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mtext>sub</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>l</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:msub><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad5c56ieqn2.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, of cumulative (time-integrated) currents up to time <italic toggle=\"yes\">T</italic> across the <italic toggle=\"yes\">i</italic>th bond and across a subsystem of size <italic toggle=\"yes\">l</italic> (summed over bonds in the subsystem), respectively. We also calculate the (two-point) dynamic correlation function of the subsystem mass. In particular, we show that, for large <inline-formula>\u0000<tex-math><?CDATA $L gg 1$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mi>L</mml:mi><mml:mo>≫</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad5c56ieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula>, the second cumulant <inline-formula>\u0000<tex-math><?CDATA $langle mathcal{Q}_i^2(T) rangle_c$?></tex-math>\u0000<mml:math overflow=\"scroll\"><mml:mrow><mml:mo fence=\"false\" stretchy=\"false\">⟨</mml:mo><mml:msubsup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mi>i</mml:mi><mml:mn>2</mml:mn></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy=\"false\">)</mml:mo><mml:msub><mml:mo fence=\"false\" stretchy=\"false\">⟩</mml:mo><mml:mi>c</mml:mi></mml:msub></mml:mrow></mml:math>\u0000<inline-graphic xlink:href=\"jstatad5c56ieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\u0000</inline-formula> of the cumulative current up to time <italic ","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"70 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-12DOI: 10.1088/1742-5468/ad64bb
Natalia Ruiz-Pino, Antonio Prados
In feedback-controlled systems, an external agent—the feedback controller—measures the state of the system and modifies its subsequent dynamics depending on the outcome of the measurement. In this paper, we build a Markovian description for the joint stochastic process that comprises both the system and the controller variables. This Markovian description is valid for a wide class of feedback-controlled systems, allowing for the inclusion of errors in the measurement. The general framework is motivated and illustrated with the paradigmatic example of the feedback flashing ratchet.
{"title":"Markovian description of a wide class of feedback-controlled systems: application to the feedback flashing ratchet","authors":"Natalia Ruiz-Pino, Antonio Prados","doi":"10.1088/1742-5468/ad64bb","DOIUrl":"https://doi.org/10.1088/1742-5468/ad64bb","url":null,"abstract":"In feedback-controlled systems, an external agent—the feedback controller—measures the state of the system and modifies its subsequent dynamics depending on the outcome of the measurement. In this paper, we build a Markovian description for the joint stochastic process that comprises both the system and the controller variables. This Markovian description is valid for a wide class of feedback-controlled systems, allowing for the inclusion of errors in the measurement. The general framework is motivated and illustrated with the paradigmatic example of the feedback flashing ratchet.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"1 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-11DOI: 10.1088/1742-5468/ad0635
Pierfrancesco Urbani
Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.
{"title":"Quantum exploration of high-dimensional canyon landscapes","authors":"Pierfrancesco Urbani","doi":"10.1088/1742-5468/ad0635","DOIUrl":"https://doi.org/10.1088/1742-5468/ad0635","url":null,"abstract":"Canyon landscapes in high dimension can be described as manifolds of small, but extensive dimension, immersed in a higher dimensional ambient space and characterized by a zero potential energy on the manifold. Here we consider the problem of a quantum particle exploring a prototype of a high-dimensional random canyon landscape. We characterize the thermal partitionfunction and show that around the point where the classical phase space has a satisfiability transition so that zero potential energy canyons disappear, moderate quantum fluctuations have a deleterious effect: they induce glassy phasesat temperature where classical thermal fluctuations alone would thermalize the system. Surprisingly we show that even when, classically, diffusion is expected to be unbounded in space, the interplay between quantum fluctuations and the randomness of the canyon landscape conspire to have a confining effect.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"45 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945003","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-07DOI: 10.1088/1742-5468/ad6428
David Martin, Gianmarco Spera, Hugues Chaté, Charlie Duclut, Cesare Nardini, Julien Tailleur and Frédéric van Wijland
The nature of the transition to collective motion in assemblies of aligning self-propelled particles remains a long-standing matter of debate. In this article, we focus on dry active matter and show that weak fluctuations suffice to generically turn second-order mean-field transitions into a ‘discontinuous’ coexistence scenario. Our theory shows how fluctuations induce a density-dependence of the polar-field mass, even when this effect is absent at mean-field level. In turn, this dependency on density triggers a feedback loop between ordering and advection that ultimately leads to an inhomogeneous transition to collective motion and the emergence of inhomogeneous travelling bands. Importantly, we show that such a fluctuation-induced first order transition is present in both metric models, in which particles align with neighbors within a finite distance, and in ‘topological’ ones, in which alignment is based on more complex constructions of neighbor sets. We compute analytically the noise-induced renormalization of the polar-field mass using stochastic calculus, which we further back up by a one-loop field-theoretical analysis. Finally, we confirm our analytical predictions by numerical simulations of fluctuating hydrodynamics as well as of topological particle models with either k-nearest neighbors or Voronoi alignment.
在对齐自走粒子的集合体中，向集体运动过渡的性质仍是一个长期争论的问题。在这篇文章中，我们将重点放在干活性物质上，并证明微弱的波动足以将二阶平均场过渡转变为 "不连续 "共存情景。我们的理论展示了波动是如何诱发极场质量的密度依赖性的，即使这种效应在均场水平上并不存在。反过来，这种对密度的依赖会引发有序和平流之间的反馈回路，最终导致向集体运动的非均质过渡和非均质旅行带的出现。重要的是，我们证明了这种由波动引起的一阶转变既存在于粒子与相邻粒子在有限距离内对齐的度量模型中，也存在于 "拓扑 "模型中，其中对齐是基于更复杂的相邻集合构造。我们利用随机微积分对噪声引起的极场质量重正化进行了分析计算，并通过一回路场理论分析进一步予以支持。最后，我们通过对波动流体力学以及具有 k 近邻或 Voronoi 排列的拓扑粒子模型进行数值模拟，证实了我们的分析预测。
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Pub Date : 2024-08-01DOI: 10.1088/1742-5468/ad6138
Indrani Bose
The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction of the output of a production function and the technology efficiency parameter , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital . We derive analytically the steady state probability distribution and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of We identify a critical value of below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.
{"title":"Growth, poverty trap and escape","authors":"Indrani Bose","doi":"10.1088/1742-5468/ad6138","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6138","url":null,"abstract":"The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction of the output of a production function and the technology efficiency parameter , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital . We derive analytically the steady state probability distribution and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of We identify a critical value of below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"42 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141881079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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