Pub Date : 2024-09-03DOI: 10.1088/1742-5468/ad6134
Mathis Guéneau, Léo Touzo
We consider a generic one-dimensional stochastic process <italic toggle="yes">x</italic>(<italic toggle="yes">t</italic>), or a random walk <italic toggle="yes">X<sub>n</sub></italic>, which describes the position of a particle evolving inside an interval <inline-formula> <tex-math><?CDATA $[a,b]$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mo stretchy="false">[</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy="false">]</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6134ieqn1.gif"></inline-graphic></inline-formula>, with absorbing walls located at <italic toggle="yes">a</italic> and <italic toggle="yes">b</italic>. In continuous time, <italic toggle="yes">x</italic>(<italic toggle="yes">t</italic>) is driven by some equilibrium process <inline-formula> <tex-math><?CDATA ${boldsymbol theta}(t)$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mi mathvariant="bold-italic">θ</mml:mi></mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6134ieqn2.gif"></inline-graphic></inline-formula>, while in discrete time, the jumps of <italic toggle="yes">X<sub>n</sub></italic> follow a stationary process that obeys a time-reversal property. An important observable to characterize its behavior is the exit probability <inline-formula> <tex-math><?CDATA $E_b(x,t)$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6134ieqn3.gif"></inline-graphic></inline-formula>, which is the probability for the particle to be absorbed first at the wall <italic toggle="yes">b</italic>, before or at time <italic toggle="yes">t</italic>, given its initial position <italic toggle="yes">x</italic>. In this paper we show that the derivation of this quantity can be tackled by studying a dual process <italic toggle="yes">y</italic>(<italic toggle="yes">t</italic>) very similar to <italic toggle="yes">x</italic>(<italic toggle="yes">t</italic>) but with hard walls at <italic toggle="yes">a</italic> and <italic toggle="yes">b</italic>. More precisely, we show that the quantity <inline-formula> <tex-math><?CDATA $E_b(x,t)$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6134ieqn4.gif"></inline-graphic></inline-formula> for the process <italic toggle="yes">x</italic>(<italic toggle="yes">t</italic>) is equal to the probability <inline-formula> <tex-math><?CDATA $tilde Phi(x,t|b)$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mrow><mml:mover
我们考虑一个通用的一维随机过程 x(t)或随机游走 Xn，它描述了一个粒子在区间 [a,b] 内演化的位置，吸收墙位于 a 和 b 处。在连续时间内，x(t) 由某个均衡过程 θ(t) 驱动，而在离散时间内，Xn 的跳跃遵循一个服从时间反转特性的静止过程。描述其行为特征的一个重要观测指标是出口概率 Eb(x,t)，即粒子在给定其初始位置 x 的情况下，在时间 t 之前或 t 时首先被壁 b 吸收的概率。在本文中，我们将展示如何通过研究与 x(t) 非常相似但在 a 和 b 处有硬壁的对偶过程 y(t) 来解决这个问题。更准确地说，我们将展示过程 x(t) 的 Eb(x,t) 等价于在时间 t 在区间 [a,x] 内找到对偶过程的概率 Φ~(x,t|b)，其中 y(0)=b 。这在数学中被称为西格蒙德对偶性。在这里，我们将证明这种对偶性适用于物理学中各种令人感兴趣的过程，包括活动粒子模型、扩散弥散模型、一大类离散和连续时间随机漫步，甚至是受随机重置影响的过程。对于所有这些情况，我们都提供了对偶过程的明确构造。我们还给出了连续和离散时间背景下这一特性的简单推导，以及大量相关模型的数值检验。最后，我们通过模拟来证明，对于更复杂的过程，如分数布朗运动，对偶性也可能成立。
{"title":"Siegmund duality for physicists: a bridge between spatial and first-passage properties of continuous- and discrete-time stochastic processes","authors":"Mathis Guéneau, Léo Touzo","doi":"10.1088/1742-5468/ad6134","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6134","url":null,"abstract":"We consider a generic one-dimensional stochastic process <italic toggle=\"yes\">x</italic>(<italic toggle=\"yes\">t</italic>), or a random walk <italic toggle=\"yes\">X<sub>n</sub></italic>, which describes the position of a particle evolving inside an interval <inline-formula>\u0000<tex-math><?CDATA $[a,b]$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mo stretchy=\"false\">[</mml:mo><mml:mi>a</mml:mi><mml:mo>,</mml:mo><mml:mi>b</mml:mi><mml:mo stretchy=\"false\">]</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6134ieqn1.gif\"></inline-graphic></inline-formula>, with absorbing walls located at <italic toggle=\"yes\">a</italic> and <italic toggle=\"yes\">b</italic>. In continuous time, <italic toggle=\"yes\">x</italic>(<italic toggle=\"yes\">t</italic>) is driven by some equilibrium process <inline-formula>\u0000<tex-math><?CDATA ${boldsymbol theta}(t)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mi mathvariant=\"bold-italic\">θ</mml:mi></mml:mrow><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6134ieqn2.gif\"></inline-graphic></inline-formula>, while in discrete time, the jumps of <italic toggle=\"yes\">X<sub>n</sub></italic> follow a stationary process that obeys a time-reversal property. An important observable to characterize its behavior is the exit probability <inline-formula>\u0000<tex-math><?CDATA $E_b(x,t)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6134ieqn3.gif\"></inline-graphic></inline-formula>, which is the probability for the particle to be absorbed first at the wall <italic toggle=\"yes\">b</italic>, before or at time <italic toggle=\"yes\">t</italic>, given its initial position <italic toggle=\"yes\">x</italic>. In this paper we show that the derivation of this quantity can be tackled by studying a dual process <italic toggle=\"yes\">y</italic>(<italic toggle=\"yes\">t</italic>) very similar to <italic toggle=\"yes\">x</italic>(<italic toggle=\"yes\">t</italic>) but with hard walls at <italic toggle=\"yes\">a</italic> and <italic toggle=\"yes\">b</italic>. More precisely, we show that the quantity <inline-formula>\u0000<tex-math><?CDATA $E_b(x,t)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>E</mml:mi><mml:mi>b</mml:mi></mml:msub><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:mi>t</mml:mi><mml:mo stretchy=\"false\">)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6134ieqn4.gif\"></inline-graphic></inline-formula> for the process <italic toggle=\"yes\">x</italic>(<italic toggle=\"yes\">t</italic>) is equal to the probability <inline-formula>\u0000<tex-math><?CDATA $tilde Phi(x,t|b)$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:mover","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"28 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188499","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 : 2024-08-30DOI: 10.1088/1742-5468/ad6c2d
Mingnan Ding, Jun Wu, Xiangjun Xing
In this work, we study the stochastic dynamics of micro-magnetics interacting with a spin-current torque. We extend the previously constructed stochastic Landau–Lifshitz equation to the case with spin-current torque, and verify the conditions of detailed balance. Then we construct various thermodynamics quantities such as work and heat, and prove the second law of thermodynamics. Due to the existence of spin-torque and the asymmetry of the kinetic matrix, a novel effect of entropy pumping shows up. As a consequence, the system may behave as a heat engine which constantly transforms heat into magnetic work. Finally, we derive a fluctuation theorem for the joint probability density function of the pumped entropy and the total work, and verify it using numerical simulations.
{"title":"Stochastic thermodynamics of micromagnetics with spin torque","authors":"Mingnan Ding, Jun Wu, Xiangjun Xing","doi":"10.1088/1742-5468/ad6c2d","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c2d","url":null,"abstract":"In this work, we study the stochastic dynamics of micro-magnetics interacting with a spin-current torque. We extend the previously constructed stochastic Landau–Lifshitz equation to the case with spin-current torque, and verify the conditions of detailed balance. Then we construct various thermodynamics quantities such as work and heat, and prove the second law of thermodynamics. Due to the existence of spin-torque and the asymmetry of the kinetic matrix, a novel effect of <italic toggle=\"yes\">entropy pumping</italic> shows up. As a consequence, the system may behave as a heat engine which constantly transforms heat into magnetic work. Finally, we derive a fluctuation theorem for the joint probability density function of the pumped entropy and the total work, and verify it using numerical simulations.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"60 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188501","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 : 2024-08-30DOI: 10.1088/1742-5468/ad6975
M Ali Saif
We study the crossover phenomena from the dynamical percolation class (DyP) to the directed percolation class (DP) in the model of disease spreading, susceptible-infected-refractory-susceptible (SIRS) on a two-dimensional lattice. In this model, agents of three species <italic toggle="yes">S</italic>, <italic toggle="yes">I</italic>, and <italic toggle="yes">R</italic> on a lattice react as follows: <inline-formula> <tex-math><?CDATA $S+Irightarrow I+I$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mi>S</mml:mi><mml:mo>+</mml:mo><mml:mi>I</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:mi>I</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6975ieqn1.gif"></inline-graphic></inline-formula> with probability <italic toggle="yes">λ</italic>, <inline-formula> <tex-math><?CDATA $Irightarrow R$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6975ieqn2.gif"></inline-graphic></inline-formula> after infection time <italic toggle="yes">τ</italic><sub><italic toggle="yes">I</italic></sub> and <inline-formula> <tex-math><?CDATA $Rrightarrow I$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mi>R</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>I</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6975ieqn3.gif"></inline-graphic></inline-formula> after recovery time <italic toggle="yes">τ</italic><sub><italic toggle="yes">R</italic></sub>. Depending on the value of the parameter <italic toggle="yes">τ</italic><sub><italic toggle="yes">R</italic></sub>, the SIRS model can be reduced to the following two well-known special cases. On the one hand, when <inline-formula> <tex-math><?CDATA $tau_R rightarrow 0$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6975ieqn4.gif"></inline-graphic></inline-formula>, the SIRS model reduces to the SIS model. On the other hand, when <inline-formula> <tex-math><?CDATA $tau_R rightarrow infty$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi mathvariant="normal">∞</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6975ieqn5.gif"></inline-graphic></inline-formula> the model reduces to the SIR model. It is known that whereas the SIS model belongs to the DP universality class, the SIR model belongs to the DyP universality class. We can deduce from the model dynamics that SIRS will behave as the SIS model for any finite values of <italic toggle="yes">τ</italic><sub><italic toggle="yes">R</italic></sub>. The model will behave as SIR only when <inline-formula> <tex-math><?CDATA $tau_R = infty$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:m
{"title":"The crossover from a dynamical percolation class to a directed percolation class on a two dimensional lattice","authors":"M Ali Saif","doi":"10.1088/1742-5468/ad6975","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6975","url":null,"abstract":"We study the crossover phenomena from the dynamical percolation class (DyP) to the directed percolation class (DP) in the model of disease spreading, susceptible-infected-refractory-susceptible (SIRS) on a two-dimensional lattice. In this model, agents of three species <italic toggle=\"yes\">S</italic>, <italic toggle=\"yes\">I</italic>, and <italic toggle=\"yes\">R</italic> on a lattice react as follows: <inline-formula>\u0000<tex-math><?CDATA $S+Irightarrow I+I$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>S</mml:mi><mml:mo>+</mml:mo><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>I</mml:mi><mml:mo>+</mml:mo><mml:mi>I</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6975ieqn1.gif\"></inline-graphic></inline-formula> with probability <italic toggle=\"yes\">λ</italic>, <inline-formula>\u0000<tex-math><?CDATA $Irightarrow R$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>I</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>R</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6975ieqn2.gif\"></inline-graphic></inline-formula> after infection time <italic toggle=\"yes\">τ</italic><sub><italic toggle=\"yes\">I</italic></sub> and <inline-formula>\u0000<tex-math><?CDATA $Rrightarrow I$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mi>R</mml:mi><mml:mo stretchy=\"false\">→</mml:mo><mml:mi>I</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6975ieqn3.gif\"></inline-graphic></inline-formula> after recovery time <italic toggle=\"yes\">τ</italic><sub><italic toggle=\"yes\">R</italic></sub>. Depending on the value of the parameter <italic toggle=\"yes\">τ</italic><sub><italic toggle=\"yes\">R</italic></sub>, the SIRS model can be reduced to the following two well-known special cases. On the one hand, when <inline-formula>\u0000<tex-math><?CDATA $tau_R rightarrow 0$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo stretchy=\"false\">→</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6975ieqn4.gif\"></inline-graphic></inline-formula>, the SIRS model reduces to the SIS model. On the other hand, when <inline-formula>\u0000<tex-math><?CDATA $tau_R rightarrow infty$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mi>R</mml:mi></mml:msub><mml:mo stretchy=\"false\">→</mml:mo><mml:mi mathvariant=\"normal\">∞</mml:mi></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6975ieqn5.gif\"></inline-graphic></inline-formula> the model reduces to the SIR model. It is known that whereas the SIS model belongs to the DP universality class, the SIR model belongs to the DyP universality class. We can deduce from the model dynamics that SIRS will behave as the SIS model for any finite values of <italic toggle=\"yes\">τ</italic><sub><italic toggle=\"yes\">R</italic></sub>. The model will behave as SIR only when <inline-formula>\u0000<tex-math><?CDATA $tau_R = infty$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:m","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"45 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188500","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 : 2024-08-30DOI: 10.1088/1742-5468/ad6c2f
Mingnan Ding, Jun Wu, Xiangjun Xing
In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into the Landau–Lifshitz (LL) equation, which describes the irreversible and deterministic dynamics of magnetic moments. The resulting stochastic LL equation obeys detailed balance, which guarantees that, with the external field fixed, the system converges to thermodynamic equilibrium with vanishing entropy production and with non-vanishing probability current. We then discuss various thermodynamic variables both at the trajectory level and at the ensemble level, and further establish both the first and the second laws of thermodynamics. Finally, we establish the Crooks fluctuation theorem, and verify it using numerical simulations.
{"title":"Stochastic thermodynamics of micromagnetics","authors":"Mingnan Ding, Jun Wu, Xiangjun Xing","doi":"10.1088/1742-5468/ad6c2f","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c2f","url":null,"abstract":"In this work, we study the stochastic thermodynamics of micro-magnetic systems. We first formulate the stochastic dynamics of micro-magnetic systems by incorporating noises into the Landau–Lifshitz (LL) equation, which describes the irreversible and deterministic dynamics of magnetic moments. The resulting stochastic LL equation obeys detailed balance, which guarantees that, with the external field fixed, the system converges to thermodynamic equilibrium with vanishing entropy production and with non-vanishing probability current. We then discuss various thermodynamic variables both at the trajectory level and at the ensemble level, and further establish both the first and the second laws of thermodynamics. Finally, we establish the Crooks fluctuation theorem, and verify it using numerical simulations.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"23 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188502","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 : 2024-08-28DOI: 10.1088/1742-5468/ad6133
Shashank Prakash, Urna Basu, Sanjib Sabhapandit
We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant <italic toggle="yes">k</italic>, rotation diffusion coefficient <italic toggle="yes">D</italic><sub><italic toggle="yes">R</italic></sub>, and directional reversal rate <italic toggle="yes">γ</italic>. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time-scales, <inline-formula> <tex-math><?CDATA $k^{-1}, D_R^{-1}$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>R</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6133ieqn1.gif"></inline-graphic></inline-formula> and <italic toggle="yes">γ</italic><sup>−1</sup>, the strength of the spring constant <italic toggle="yes">k</italic> relative to <italic toggle="yes">D</italic><sub><italic toggle="yes">R</italic></sub> and <italic toggle="yes">γ</italic> gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth <italic toggle="yes">t</italic><sup><italic toggle="yes">ν</italic></sup>, where the value of the exponent <italic toggle="yes">ν</italic> depends on the specific regime. For a quenched initial orientation, the exponent <italic toggle="yes">ν</italic> crosses over from 3 to <inline-formula> <tex-math><?CDATA $1/2$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6133ieqn2.gif"></inline-graphic></inline-formula>, via intermediate values <inline-formula> <tex-math><?CDATA $5/2$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mn>5</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6133ieqn3.gif"></inline-graphic></inline-formula> or 1, depending on the specific coupling limits. However, for the annealed initial orientation, <italic toggle="yes">ν</italic> crosses over from 2 to <inline-formula> <tex-math><?CDATA $1/2$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6133ieqn4.gif"></inline-graphic></inline-formula> via an intermediate value <inline-formula> <tex-math><?CDATA $3/2$?></tex-math><mml:math overflow="scroll"><mml:mrow><mml:mn>3</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="jstatad6133ieqn5.gif"></inline-graphic></inline-formula> or 1 for the
{"title":"Tagged particle behavior in a harmonic chain of direction-reversing active Brownian particles","authors":"Shashank Prakash, Urna Basu, Sanjib Sabhapandit","doi":"10.1088/1742-5468/ad6133","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6133","url":null,"abstract":"We study the tagged particle dynamics in a harmonic chain of direction-reversing active Brownian particles, with the spring constant <italic toggle=\"yes\">k</italic>, rotation diffusion coefficient <italic toggle=\"yes\">D</italic><sub><italic toggle=\"yes\">R</italic></sub>, and directional reversal rate <italic toggle=\"yes\">γ</italic>. We exactly compute the tagged particle position variance for quenched and annealed initial orientations of the particles. For well-separated time-scales, <inline-formula>\u0000<tex-math><?CDATA $k^{-1}, D_R^{-1}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msup><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup><mml:mo>,</mml:mo><mml:msubsup><mml:mi>D</mml:mi><mml:mi>R</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn1.gif\"></inline-graphic></inline-formula> and <italic toggle=\"yes\">γ</italic><sup>−1</sup>, the strength of the spring constant <italic toggle=\"yes\">k</italic> relative to <italic toggle=\"yes\">D</italic><sub><italic toggle=\"yes\">R</italic></sub> and <italic toggle=\"yes\">γ</italic> gives rise to different coupling limits, and for each coupling limit there are short, intermediate, and long-time regimes. In the thermodynamic limit, we show that, to the leading order, the tagged particle variance exhibits an algebraic growth <italic toggle=\"yes\">t</italic><sup><italic toggle=\"yes\">ν</italic></sup>, where the value of the exponent <italic toggle=\"yes\">ν</italic> depends on the specific regime. For a quenched initial orientation, the exponent <italic toggle=\"yes\">ν</italic> crosses over from 3 to <inline-formula>\u0000<tex-math><?CDATA $1/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn2.gif\"></inline-graphic></inline-formula>, via intermediate values <inline-formula>\u0000<tex-math><?CDATA $5/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>5</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn3.gif\"></inline-graphic></inline-formula> or 1, depending on the specific coupling limits. However, for the annealed initial orientation, <italic toggle=\"yes\">ν</italic> crosses over from 2 to <inline-formula>\u0000<tex-math><?CDATA $1/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn4.gif\"></inline-graphic></inline-formula> via an intermediate value <inline-formula>\u0000<tex-math><?CDATA $3/2$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mn>3</mml:mn><mml:mrow><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6133ieqn5.gif\"></inline-graphic></inline-formula> or 1 for the","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"7 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188521","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 : 2024-08-28DOI: 10.1088/1742-5468/ad5271
Louis Saddier, Matteo Marsili
The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.
{"title":"A Bayesian theory of market impact","authors":"Louis Saddier, Matteo Marsili","doi":"10.1088/1742-5468/ad5271","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5271","url":null,"abstract":"The available liquidity at any time in financial markets falls largely short of the typical size of the orders that institutional investors would trade. In order to reduce the impact on prices due to the execution of large orders, traders in financial markets split large orders into a series of smaller ones, which are executed sequentially. The resulting sequence of trades is called a meta-order. Empirical studies have revealed a non-trivial set of statistical laws on how meta-orders affect prices, which include (i) the square-root behaviour of the expected price variation with the total volume traded, (ii) its crossover to a linear regime for small volumes and (iii) a reversion of average prices towards its initial value, after the sequence of trades is over. Here we recover this phenomenology within a minimal theoretical framework where the market sets prices by incorporating all information on the direction and speed of trade of the meta-order in a Bayesian manner. The simplicity of this derivation lends further support to the robustness and universality of market impact laws. In particular, it suggests that the square-root impact law originates from over-estimation of order flows originating from meta-orders.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"50 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188520","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 : 2024-08-22DOI: 10.1088/1742-5468/ad6c30
Wenhui Wang, Juping Zhang, Maoxing Liu, Zhen Jin
To describe the dynamics of epidemic spread with multiple individuals interacting with each other, we develop a susceptible-infected-susceptible (SIS) spread model with collective and individual contagion in general hypernetworks with higher-order interactions. The constructed model is applied to a bi-uniform hypernetwork to obtain a mean-field model for the SIS model. The threshold value at which an epidemic can spread in the bi-uniform hypernetwork is obtained and analyzed dynamically. By analysis, the model leads to bistability, in which a disease-free equilibrium and an endemic equilibrium coexist. Finally, numerical simulations of the developed model are carried out to give the effect of the proportion of individual contagion hyperedges on the spread of an epidemic.
{"title":"Analysis of SIS epidemic model in bi-uniform hypernetworks","authors":"Wenhui Wang, Juping Zhang, Maoxing Liu, Zhen Jin","doi":"10.1088/1742-5468/ad6c30","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c30","url":null,"abstract":"To describe the dynamics of epidemic spread with multiple individuals interacting with each other, we develop a susceptible-infected-susceptible (SIS) spread model with collective and individual contagion in general hypernetworks with higher-order interactions. The constructed model is applied to a bi-uniform hypernetwork to obtain a mean-field model for the SIS model. The threshold value at which an epidemic can spread in the bi-uniform hypernetwork is obtained and analyzed dynamically. By analysis, the model leads to bistability, in which a disease-free equilibrium and an endemic equilibrium coexist. Finally, numerical simulations of the developed model are carried out to give the effect of the proportion of individual contagion hyperedges on the spread of an epidemic.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"2010 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188524","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 : 2024-08-22DOI: 10.1088/1742-5468/ad6c2e
Leonardo Lenzini, Giuseppe Fava, Francesco Ginelli
We consider a flocking system confined transversally between two infinite reflecting parallel walls separated by a distance L⊥. Infinite or periodic boundary conditions are assumed longitudinally to the direction of collective motion, defining a ring geometry typical of experimental realizations with flocking active colloids. Such a confinement selects a flocking state with its mean direction aligned parallel to the wall, thus breaking explicitly the rotational symmetry locally by a boundary effect. Finite size scaling analysis and numerical simulations show that confinement induces an effective mass term Mc∼L⊥−ζ (with positive ζ being equal to the dynamical scaling exponent of the free theory) suppressing scale free correlations at small wave-numbers. However, due to the finite system size in the transversal direction, this effect can only be detected for large enough longitudinal system sizes (i.e. narrow ring geometries). Furthermore, in the longitudinal direction, density correlations are characterized by an anomalous effective mass term. The effective mass term also enhances the global scalar order parameter and suppresses fluctuations of the mean flocking direction. These results suggest an equivalence between transversal confinement and driving by an homogeneous external field, which breaks the rotational symmetry at the global level.
{"title":"Boundary symmetry breaking of flocking systems","authors":"Leonardo Lenzini, Giuseppe Fava, Francesco Ginelli","doi":"10.1088/1742-5468/ad6c2e","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6c2e","url":null,"abstract":"We consider a flocking system confined transversally between two infinite reflecting parallel walls separated by a distance <inline-formula>\u0000<tex-math><?CDATA $L_perp$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:msub><mml:mi>L</mml:mi><mml:mo>⊥</mml:mo></mml:msub></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6c2eieqn1.gif\"></inline-graphic></inline-formula>. Infinite or periodic boundary conditions are assumed longitudinally to the direction of collective motion, defining a ring geometry typical of experimental realizations with flocking active colloids. Such a confinement selects a flocking state with its mean direction aligned parallel to the wall, thus breaking explicitly the rotational symmetry locally by a boundary effect. Finite size scaling analysis and numerical simulations show that confinement induces an effective mass term <inline-formula>\u0000<tex-math><?CDATA ${M_c} sim L_perp^{-zeta}$?></tex-math><mml:math overflow=\"scroll\"><mml:mrow><mml:mrow><mml:msub><mml:mi>M</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:mrow><mml:mo>∼</mml:mo><mml:msubsup><mml:mi>L</mml:mi><mml:mo>⊥</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mi>ζ</mml:mi></mml:mrow></mml:msubsup></mml:mrow></mml:math><inline-graphic xlink:href=\"jstatad6c2eieqn2.gif\"></inline-graphic></inline-formula> (with positive <italic toggle=\"yes\">ζ</italic> being equal to the dynamical scaling exponent of the free theory) suppressing scale free correlations at small wave-numbers. However, due to the finite system size in the transversal direction, this effect can only be detected for large enough longitudinal system sizes (i.e. narrow ring geometries). Furthermore, in the longitudinal direction, density correlations are characterized by an anomalous effective mass term. The effective mass term also enhances the global scalar order parameter and suppresses fluctuations of the mean flocking direction. These results suggest an equivalence between transversal confinement and driving by an homogeneous external field, which breaks the rotational symmetry at the global level.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"30 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188526","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 : 2024-08-22DOI: 10.1088/1742-5468/ad5c59
Janik Schüttler, Robert L Jack, Michael E Cates
We study the effect of phase-separating diffusive dynamics on the mean time to extinction (MTE) in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual particles on two sites undergo on-site reactions and hopping between the sites. In the slow-reaction limit, we project the models’ dynamics onto suitable one-dimensional reaction coordinates, which allows the derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the MTE. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We discuss how Allee effects can be affected by phase separation, including situations where the tendency to phase-separate renders an otherwise stable population unstable.
我们研究了在几种慢反应的反应扩散模型中，相分离扩散动力学对平均消亡时间（MTE）的影响。我们考虑了类似于 AB 模型的连续体理论，以及两个位点上的单个粒子发生现场反应并在位点间跳跃的简单模型。在慢反应极限，我们将模型的动力学投影到合适的一维反应坐标上，从而推导出准平衡有效自由能。对于弱噪声，这就能确定 MTE 的特征。与同质参考情况相比，相分离的加入可以增强或抑制这一时间。我们将讨论相分离如何影响阿利效应，包括相分离趋势使原本稳定的种群变得不稳定的情况。
{"title":"Effects of phase separation on extinction times in population models","authors":"Janik Schüttler, Robert L Jack, Michael E Cates","doi":"10.1088/1742-5468/ad5c59","DOIUrl":"https://doi.org/10.1088/1742-5468/ad5c59","url":null,"abstract":"We study the effect of phase-separating diffusive dynamics on the mean time to extinction (MTE) in several reaction-diffusion models with slow reactions. We consider a continuum theory similar to model AB, and a simple model where individual particles on two sites undergo on-site reactions and hopping between the sites. In the slow-reaction limit, we project the models’ dynamics onto suitable one-dimensional reaction coordinates, which allows the derivation of quasi-equilibrium effective free energies. For weak noise, this enables characterisation of the MTE. This time can be enhanced or suppressed by the addition of phase separation, compared with homogeneous reference cases. We discuss how Allee effects can be affected by phase separation, including situations where the tendency to phase-separate renders an otherwise stable population unstable.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"8 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188522","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 : 2024-08-22DOI: 10.1088/1742-5468/ad6977
Djordje Spasojević, Sanja Janićević
We report the findings of an extensive and systematic study on the effect of crystal grain size on the response of field-driven disordered ferromagnetic systems with thin, intermediate, and bulk geometry. For numerical modeling we used the athermal nonequilibrium variant of the random field Ising model simulating the systems with tightly packed and uniformly cubic-shaped, magnetically exchange-coupled crystal grains, conducted over a wide range of grain sizes. Together with the standard hysteresis loop characterizations, we offer an in-depth examination of the avalanching response of the system, estimating the effective grain-size-related exponents by analyses of the distributions of various avalanche parameters, average avalanche shape and size, and power spectra. Our results demonstrate that grain size plays an important role in the behavior of the system, outweighing the effect of its geometry. For sufficiently small grains, the characteristics of the system response are largely unaffected by grain size; however, for larger grains, the effects become more noticeable and show up as distinct asymmetry in the magnetization susceptibilities and average avalanche shapes, as well as characteristic kinks in the distributions of avalanche parameters, susceptibilities, and magnetizations for the largest grain sizes. Our insights, unveiling the sensitivity of the system’s response to the underlying structure in terms of crystal grain size, may prove beneficial in interpreting and analyzing experimental results obtained from driven disordered ferromagnetic samples of different geometries, as well as in extending the range of possible applications.
{"title":"The impact of crystal grain size on the behavior of disordered ferromagnetic systems: from thin to bulk geometry","authors":"Djordje Spasojević, Sanja Janićević","doi":"10.1088/1742-5468/ad6977","DOIUrl":"https://doi.org/10.1088/1742-5468/ad6977","url":null,"abstract":"We report the findings of an extensive and systematic study on the effect of crystal grain size on the response of field-driven disordered ferromagnetic systems with thin, intermediate, and bulk geometry. For numerical modeling we used the athermal nonequilibrium variant of the random field Ising model simulating the systems with tightly packed and uniformly cubic-shaped, magnetically exchange-coupled crystal grains, conducted over a wide range of grain sizes. Together with the standard hysteresis loop characterizations, we offer an in-depth examination of the avalanching response of the system, estimating the effective grain-size-related exponents by analyses of the distributions of various avalanche parameters, average avalanche shape and size, and power spectra. Our results demonstrate that grain size plays an important role in the behavior of the system, outweighing the effect of its geometry. For sufficiently small grains, the characteristics of the system response are largely unaffected by grain size; however, for larger grains, the effects become more noticeable and show up as distinct asymmetry in the magnetization susceptibilities and average avalanche shapes, as well as characteristic kinks in the distributions of avalanche parameters, susceptibilities, and magnetizations for the largest grain sizes. Our insights, unveiling the sensitivity of the system’s response to the underlying structure in terms of crystal grain size, may prove beneficial in interpreting and analyzing experimental results obtained from driven disordered ferromagnetic samples of different geometries, as well as in extending the range of possible applications.","PeriodicalId":17207,"journal":{"name":"Journal of Statistical Mechanics: Theory and Experiment","volume":"9 1","pages":""},"PeriodicalIF":2.4,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142188523","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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