S. N. Bose National Centre for Basic Sciences, Kolkata 700106, India.
Raman Research Institute, Bengaluru 560080, India.
Phys Rev E. 2023 Jan;107(1-1):014123. doi: 10.1103/PhysRevE.107.014123.
We study the stationary state of a chain of harmonic oscillators driven by two active reservoirs at the two ends. These reservoirs exert correlated stochastic forces on the boundary oscillators which eventually leads to a nonequilibrium stationary state of the system. We consider three most well-known dynamics for the active force, namely, the active Ornstein-Uhlenbeck process, run-and-tumble process, and active Brownian process, all of which have exponentially decaying two-point temporal correlations but very different higher-order fluctuations. We show that, irrespective of the specific dynamics of the drive, the stationary velocity fluctuations are Gaussian in nature with a kinetic temperature which remains uniform in the bulk. Moreover, we find the emergence of an "equipartition of energy" in the bulk of the system-the bulk kinetic temperature equals the bulk potential temperature in the thermodynamic limit. We also calculate the stationary distribution of the instantaneous energy current in the bulk which always shows a logarithmic divergence near the origin and asymmetric exponential tails. The signatures of specific active driving become visible in the behavior of the oscillators near the boundary. This is most prominent for the RTP- and ABP-driven chains where the boundary velocity distributions become non-Gaussian and the current distribution has a finite cutoff.
我们研究了由两个活性储层在两端驱动的谐振子链的稳态。这些储层对边界谐振子施加相关的随机力，最终导致系统达到非平衡稳态。我们考虑了主动力最著名的三种动力学，即主动 Ornstein-Uhlenbeck 过程、跑跳过程和主动布朗运动，它们都具有指数衰减的两点时间相关，但具有非常不同的高阶涨落。我们表明，无论驱动的具体动力学如何，稳态速度涨落本质上是高斯分布的，其动力学温度在体相保持均匀。此外，我们发现系统体相出现了“能量均分”-在热力学极限下，体相动力学温度等于体相势能温度。我们还计算了体相瞬时能量流的稳态分布，该分布在原点附近总是表现出对数发散和非对称指数尾部。特定主动驱动的特征在边界附近的振荡器行为中变得明显。对于 RTP 和 ABP 驱动的链来说，这种情况最为明显，边界速度分布变得非高斯，电流分布具有有限的截止值。
