排列时间不可逆性是量化复杂系统非平衡特征的重要方法,但排列类型无法表征序列的精确结构特征.本文提出了一种模糊排列时间不可逆(fuzzy permutation time irreversibility,fpTIR)方法,利用负指数函数转化向量元素差值,计算向量幅度排...排列时间不可逆性是量化复杂系统非平衡特征的重要方法,但排列类型无法表征序列的精确结构特征.本文提出了一种模糊排列时间不可逆(fuzzy permutation time irreversibility,fpTIR)方法,利用负指数函数转化向量元素差值,计算向量幅度排列的隶属度,进而比较正反序列模糊排列的概率分布差异.作为对照,通过香农熵计算模糊排列概率分布的平均信息量,即模糊排列熵(fuzzy permutation entropy,fPEn),用以衡量系统的复杂度.本文首先利用logistic和Henon混沌系统以及一阶自回归模型构建测试序列,通过代替数据理论验证fpTIR和fPEn的有效性,然后分析PhysioNet数据库中的心衰、健康老年及健康年轻心率的复杂特征.结果表明,fpTIR可有效表征系统的非平衡性特征,并且提高了心率信号分析的准确度.由于fpTIR和fPEn采用不同的概率分布分析方法,两者在混沌序列验证中存在差异,甚至在心率信号的分析中出现相反的结果,其中fpTIR的分析结果与心率复杂度丢失理论一致.总之,本文研究不仅精准表征了序列的排列空间结构,优化了复杂系统非平衡性分析的效果,而且为从非平衡动力学和熵值复杂度两个角度探索复杂系统特征提供了新的视角和理论依据.展开更多
Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be wr...Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.展开更多
Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neur...Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.展开更多
We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method...We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.展开更多
In the last decade,the study of pressure in active matter has attracted growing attention due to its fundamental relevance to nonequilibrium statistical physics.Active matter systems are composed of particles that con...In the last decade,the study of pressure in active matter has attracted growing attention due to its fundamental relevance to nonequilibrium statistical physics.Active matter systems are composed of particles that consume energy to sustain persistent motion,which are inherently far from equilibrium.These particles can exhibit complex behaviors,including motility-induced phase separation,clustering,and anomalous stress distributions,motivating the introduction of active swim stress and swim pressure.Unlike in passive fluids,pressure in active systems emerges from momentum flux originating from swim force rather than equilibrium conservative interactions,offering a distinct perspective for understanding their mechanical response.Simple models of active Brownian particles(ABPs)have been employed in theoretical and simulation studies across both dilute and dense regimes,revealing that pressure is a state function and exhibits a nontrivial dependence on density.Together with nonequilibrium statistical concepts such as effective temperature and effective adhesion,pressure offers important insight for understanding behaviors in active matter such as sedimentation equilibrium and motility induced phase separation.Extensions of ABP models beyond their simplest form have underscored the fragility of the pressure-based equation of state,which can break down under factors such as density-dependent velocity,torque,complex boundary geometries and interactions.Building on these developments,this review provides a comprehensive survey of theoretical and experimental advances,with particular emphasis on the microscopic origins of active pressure and the mechanisms underlying the breakdown of the equation of state.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.12122515(HH)Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices(Grant No.2022B1212010008)Guangdong Basic and Applied Basic Research Foundation(Grant No.2023B1515040023)。
文摘Understanding neural dynamics is a central topic in machine learning,non-linear physics,and neuroscience.However,the dynamics are non-linear,stochastic and particularly non-gradient,i.e.,the driving force cannot be written as the gradient of a potential.These features make analytic studies very challenging.The common tool is the path integral approach or dynamical mean-field theory.Still,the drawback is that one has to solve the integro-differential or dynamical mean-field equations,which is computationally expensive and has no closed-form solutions in general.From the associated Fokker-Planck equation,the steady-state solution is generally unknown.Here,we treat searching for the fixed points as an optimization problem,and construct an approximate potential related to the speed of the dynamics,and find that searching for the ground state of this potential is equivalent to running approximate stochastic gradient dynamics or Langevin dynamics.Only in the zero temperature limit,can the distribution of the original fixed points be achieved.The resultant stationary state of the dynamics exactly follows the canonical Boltzmann measure.Within this framework,the quenched disorder intrinsic in the neural networks can be averaged out by applying the replica method,which leads naturally to order parameters for the non-equilibrium steady states.Our theory reproduces the well-known result of edge-of-chaos.Furthermore,the order parameters characterizing the continuous transition are derived,and the order parameters are explained as fluctuations and responses of the steady states.Our method thus opens the door to analytically studying the fixed-point landscape of the deterministic or stochastic high dimensional dynamics.
基金supported by Projects 12325501,12047503,and 12247104 of the National Natural Science Foundation of ChinaProject ZDRW-XX-2022-3-02 of the Chinese Academy of Sciencessupported by the Innovation Program for Quantum Science and Technology project 2021ZD0301900。
文摘Computing free energy is a fundamental problem in statistical physics.Recently,two distinct methods have been developed and have demonstrated remarkable success:the tensor-network-based contraction method and the neural-network-based variational method.Tensor networks are accurate,but their application is often limited to low-dimensional systems due to the high computational complexity in high-dimensional systems.The neural network method applies to systems with general topology.However,as a variational method,it is not as accurate as tensor networks.In this work,we propose an integrated approach,tensor-network-based variational autoregressive networks(TNVAN),that leverages the strengths of both tensor networks and neural networks:combining the variational autoregressive neural network’s ability to compute an upper bound on free energy and perform unbiased sampling from the variational distribution with the tensor network’s power to accurately compute the partition function for small sub-systems,resulting in a robust method for precisely estimating free energy.To evaluate the proposed approach,we conducted numerical experiments on spin glass systems with various topologies,including two-dimensional lattices,fully connected graphs,and random graphs.Our numerical results demonstrate the superior accuracy of our method compared to existing approaches.In particular,it effectively handles systems with longrange interactions and leverages GPU efficiency without requiring singular value decomposition,indicating great potential in tackling statistical mechanics problems and simulating high-dimensional complex systems through both tensor networks and neural networks.
基金supported by the National Natural Science Foundation of China(Grant No.11974420).
文摘We study the thermodynamic properties of the classical one-dimensional generalized nonlinear Klein-Gordon lattice model(n≥2)by using the cluster variation method with linear response theory.The results of this method are exact in the thermodynamic limit.We present the single-site reduced densityρ^((1))(z),averages such as(z^(2)),<|z^(n)|>,and<(z_(1)-z_(2))^(2)>,the specific heat C_(v),and the static correlation functions.We analyze the scaling behavior of these quantities and obtain the exact scaling powers at the low and high temperatures.Using these results,we gauge the accuracy of the projective truncation approximation for theφ^(4)lattice model.
基金financial support from the General Program of the National Natural Science Foundation of China(Grant No.12474195)the Key Project of Guangdong Provincial Department of Education(Grant No.2023ZDZX3021)the Natural Science Foundation of Guangdong Province(Grant No.2024A1515011343)。
文摘In the last decade,the study of pressure in active matter has attracted growing attention due to its fundamental relevance to nonequilibrium statistical physics.Active matter systems are composed of particles that consume energy to sustain persistent motion,which are inherently far from equilibrium.These particles can exhibit complex behaviors,including motility-induced phase separation,clustering,and anomalous stress distributions,motivating the introduction of active swim stress and swim pressure.Unlike in passive fluids,pressure in active systems emerges from momentum flux originating from swim force rather than equilibrium conservative interactions,offering a distinct perspective for understanding their mechanical response.Simple models of active Brownian particles(ABPs)have been employed in theoretical and simulation studies across both dilute and dense regimes,revealing that pressure is a state function and exhibits a nontrivial dependence on density.Together with nonequilibrium statistical concepts such as effective temperature and effective adhesion,pressure offers important insight for understanding behaviors in active matter such as sedimentation equilibrium and motility induced phase separation.Extensions of ABP models beyond their simplest form have underscored the fragility of the pressure-based equation of state,which can break down under factors such as density-dependent velocity,torque,complex boundary geometries and interactions.Building on these developments,this review provides a comprehensive survey of theoretical and experimental advances,with particular emphasis on the microscopic origins of active pressure and the mechanisms underlying the breakdown of the equation of state.
