Smith Naftali R
Department of Environmental Physics, Blaustein Institutes for Desert Research, Ben-Gurion University of the Negev, Sede Boqer Campus, 8499000, Israel.
Phys Rev E. 2023 Aug;108(2):L022602. doi: 10.1103/PhysRevE.108.L022602.
We consider an overdamped particle with a general physical mechanism that creates noisy active movement (e.g., a run-and-tumble particle or active Brownian particle, etc.), that is confined by an external potential. Focusing on the limit in which the correlation time τ of the active noise is small, we find the nonequilibrium steady-state distribution P_{st}(X) of the particle's position X. While typical fluctuations of X follow a Boltzmann distribution with an effective temperature that is not difficult to find, the tails of P_{st}(X) deviate from a Boltzmann behavior: In the limit τ→0, they scale as P_{st}(X)∼e^{-s(X)/τ}. We calculate the large-deviation function s(X) exactly for arbitrary trapping potential and active noise in dimension d=1, by relating it to the rate function that describes large deviations of the position of the same active particle in absence of an external potential at long times. We then extend our results to d>1 assuming rotational symmetry.
我们考虑一个过阻尼粒子，其具有产生噪声主动运动的一般物理机制（例如，一个随机游走-翻滚粒子或主动布朗粒子等），该粒子受外部势的限制。聚焦于主动噪声的相关时间τ很小的极限情况，我们找到了粒子位置X的非平衡稳态分布P_st(X)。虽然X的典型涨落遵循具有不难找到的有效温度的玻尔兹曼分布，但P_st(X)的尾部偏离玻尔兹曼行为：在τ→0的极限下，它们按P_st(X)∼e^{-s(X)/τ}缩放。通过将其与描述在长时间无外部势时同一主动粒子位置的大偏差的速率函数相关联，我们精确计算了一维中任意捕获势和主动噪声下的大偏差函数s(X)。然后，我们在假设旋转对称性的情况下将结果扩展到d>1的情况。
