论文标题
周期性电势中的布朗颗粒：粗粒与精细结构
Brownian particles in periodic potentials: coarse-graining versus fine structure
论文作者
论文摘要
我们研究了在一个维度具有外部周期性电势的情况下连接到热热浴的过度阻尼颗粒的运动。当我们粗粒（即，即使用比电势周期性大的bin位置的固定位置时，从共同起源开始的散布颗粒的包装，散布颗粒的包装，收敛到以均值的位移为中心的正态分布，其均匀的位移呈均值2 d^* t $，其有效的扩散常数比有效的散射粒子更小。我们检查了这种粗粒的描述与密度的精细结构之间的相互作用，该结构由Boltzmann-Gibbs（BG）因子$ E^{ - V（X）/K_B T} $给出，后者是不可算的。我们解释了这一结果，并使用Fokker-Planck方程构建了可观察到的理论。这些可观察的物品被归类为与BG精细结构相关的，例如能量或职业时间，而其他人（如位置力矩）很长时间以来都融合到大规模描述的那些时刻。熵属于特殊类别，因为它具有粗粒且良好的结构描述。基本的热力学公式$ f = ts-e $扩展到了这个远程平衡系统。还使用来自无限的厄运理论的工具来研究了恒星特性。
We study the motion of an overdamped particle connected to a thermal heat bath in the presence of an external periodic potential in one dimension. When we coarse-grain, i.e., bin the particle positions using bin sizes that are larger than the periodicity of the potential, the packet of spreading particles, all starting from a common origin, converges to a normal distribution centered at the origin with a mean-squared displacement that grows as $2 D^* t$, with an effective diffusion constant that is smaller than that of a freely diffusing particle. We examine the interplay between this coarse-grained description and the fine structure of the density, which is given by the Boltzmann-Gibbs (BG) factor $e^{-V(x)/k_B T}$, the latter being non-normalizable. We explain this result and construct a theory of observables using the Fokker-Planck equation. These observables are classified as those that are related to the BG fine structure, like the energy or occupation times, while others, like the positional moments, for long times, converge to those of the large-scale description. Entropy falls into a special category as it has a coarse-grained and a fine structure description. The basic thermodynamic formula $F=TS - E$ is extended to this far-from-equilibrium system. The ergodic properties are also studied using tools from infinite ergodic theory.
