标题： 与热浴接触的奔跑-翻滚粒子的稳态和弛豫动力学 显示英文标题

标题： Steady state and relaxation dynamics of run and tumble particles in contact with a heat bath

摘要： 我们研究了在一维分段线性势场$U(x)=b|x|$中运行-翻滚粒子（RTP）的弛豫动力学，从$x=0$处的δ函数初始条件到稳态。 除了经历主动电报噪声外，粒子还与温度为$T$的热浴接触，该热浴施加白热噪声。 我们发现RTP的位置分布由两种分布（“模式”）之和描述，在稳态下每种模式的形式为$P(x,t\to\infty)\sim e^{-\lambda_i|x|}$ ($i=1,2$)。 这两种模式是动态耦合的：在极短时间内（$t\to 0$），每种模式存储一半的概率，并以高斯分布表现出热扩散展宽。 随着时间的推移并向稳态演化，模式之间的概率分配变得越来越不均匀，并且根据模型参数，$\lambda_i$值较小的模式可能携带绝大多数概率。 此外，我们确定每种模式的特征弛豫时间是$\tau_i=(\lambda_i^2T)^{-1}$，这意味着少数模式也比主导模式松弛得快得多。 更详细的分析表明，$\tau_i$只在分布核心附近的原点处才是模式弛豫的特征，而在更远的地方它会随着$|x|$线性增加，就好像一个弛豫前沿以恒定速度$v_i^*=2\sqrt{T/\tau_i}$在系统中传播一样。 非平衡熵产生率可以与概率分布的双模分裂联系起来，并可以用它们的相关长度$\lambda_i$以及它们对稳态分布的贡献来表示。 显示英文摘要

摘要： We study the relaxation dynamics of a run and tumble particle in a one-dimensional piecewise linear potential $U(x)=b|x|$, from delta-function initial conditions at $x=0$ to steady state. In addition to experiencing active telegraphic noise, the particle is in contact with a heat bath at temperature $T$ that applies white thermal noise. We find that the position distribution of the RTP is described by a sum of two distributions ("modes"), each of which of the form $P(x,t\to\infty)\sim e^{-\lambda_i|x|}$ ($i=1,2$) at steady state. The two modes are dynamically coupled: At very short times ($t\to 0$), each mode stores half of the probability, and exhibits thermal diffusive spreading with a Gaussian profile. With progressing time and evolution toward steady state, the partition of probability between the modes becomes increasingly uneven and, depending on the model parameters, the mode with the smaller value of $\lambda_i$ may carry an overwhelming majority of the probability. Moreover, we identify that the characteristic relaxation time of each mode is $\tau_i=(\lambda_i^2T)^{-1}$, which implies that the minority mode also relaxes much faster than the dominant one. A more detailed analysis reveals that $\tau_i$ is characteristic of the mode relaxation only close to the origin at the core of the distribution, while further away it increases linearly with $|x|$ as if a relaxation front is propagating at constant speed $v_i^*=2\sqrt{T/\tau_i}$ in the system. The rate of non-equilibrium entropy production can be related to the two-mode splitting of the probability distribution and be expressed in terms of their correlation-lengths $\lambda_i$ and their contributions to the steady state distribution.