Summing over trajectories of stochastic dynamics with multiplicative noise

乘性噪声随机微分方程的直接数值解

Direct Numerical Solutions to Stochastic Differential Equations with Multiplicative Noise

本文受量子弛豫路径积分启发，提出一种无需轨迹平均的直接数值方法求解乘性噪声随机微分方程，并借助张量分解加速，在非马尔可夫噪声耦合振子模拟中以更低成本准确捕捉分岔转变。

协变的费米子路径积分用于具有乘性白噪声的标量朗之万过程

A covariant fermionic path integral for scalar Langevin processes with multiplicative white noise

本文提出了一种在连续时间中直接构建的协变费米子路径积分方法，用于描述具有乘性白噪声的标量朗之万过程，并推导了与高阶离散化方案一致的昂萨格-马赫鲁普公式。

轨道到Feigenbaum吸引子动力学中的q变形统计力学性质

q-Deformed Statistical-Mechanical Property in the Dynamics of Trajectories en route to the Feigenbaum Attractor

我们表明，动力学的Feigenbaum吸引子内结合起来，形成一个q-变形的物理力学建设。系综轨迹收敛到吸引子（和排斥子）的速率由从吸引子的相邻位置之间的距离求和生成的配分函数获得的q熵来描述。所涉及的q指数的值是由单峰映射普适常数给出的，而热力学结构与以前为多重分形开发的结构密切相关。作为一个重要组成部分，在我们的演示中，我们暴露，在以前未知的细节水平，轨迹的动力学的功能，无论是朝着费根鲍姆吸引或捕获其匹配的排斥。单峰映射中周期性超稳定循环族的动力学性质被认为是理解倍周期过渡到混沌时的离散尺度不变性特征的关键因素。我们明确了费根鲍姆吸引子中存在的反常热力学框架的动力学起源。

带色噪声和吸收态的随机系统：路径积分解

Stochastic System with Colored Noise and Absorbing States: Path Integral Solution

研究了一类带吸收态的乘性有色噪声随机系统的序参量$x$和共轭力涨落的振幅$ϕ$的最概然值的行为.定义了作为噪声自相关时间与温度和噪声增长速度的依赖关系的相图。结果表明，相位半平面$(x,ϕ)$可以分为隔离域的大，中，小值的$x$。用路径积分表示的概率来研究这些域中的系统行为。在区域$x\ll 1$中，对于$0 < a < 1/2$，轨迹收敛于点$x = ϕ= 0$，对于$1/2 < a \le 1$，轨迹收敛于点$x = 0$，$ϕ\to\infty$。在前一种情况下，实现轨迹的概率是有限的，而在后一种情况下，它是非常小的，可以形成一个吸收状态。

Physically consistent numerical solver for time-dependent Fokker-Planck equations

We present a simple thermodynamically consistent method for solving time-dependent Fokker--Planck equations (FPE) for over-damped stochastic processes, also known as Smoluchowski equations. It yields both transition and steady-state behavior and allows for computations of moment-generating and large-deviation functions of observables defined along stochastic trajectories, such as the fluctuating particle current, heat and work. The key strategy is to approximate the FPE by a Master equation with transition rates in configuration space that obey a local detailed balance condition for arbitrary …

Macrospin in external magnetic field: Entropy production and fluctuation theorems

We consider stochastic rotational dynamics of a macrospin at a constant temperature, in presence of an external magnetic field. Starting from the appropriate Langevin equation which contains multiplicative noise, we calculate entropy production (EP) along stochastic trajectories, and obtain fluctuation theorems. The system remains inherently out of equilibrium due to a spin torque supporting azimuthal current, leading to an excess EP apart from the EP due to heat dissipation. The anomaly may be removed using a redefinition of dissipated heat and stochastic work done. Using numerical simulation…