Herpich Tim, Shayanfard Kamran, Esposito Massimiliano
Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg.
Phys Rev E. 2020 Feb;101(2-1):022116. doi: 10.1103/PhysRevE.101.022116.
Starting from the stochastic thermodynamics description of two coupled underdamped Brownian particles, we showcase and compare three different coarse-graining schemes leading to an effective thermodynamic description for the first of the two particles: marginalization over one particle, bipartite structure with information flows, and the Hamiltonian of mean force formalism. In the limit of time-scale separation where the second particle with a fast relaxation time scale locally equilibrates with respect to the coordinates of the first slowly relaxing particle, the effective thermodynamics resulting from the first and third approach are shown to capture the full thermodynamics and to coincide with each other. In the bipartite approach, the slow part does not, in general, allow for an exact thermodynamic description as the entropic exchange between the particles is ignored. Physically, the second particle effectively becomes part of the heat reservoir. In the limit where the second particle becomes heavy and thus deterministic, the effective thermodynamics of the first two coarse-graining methods coincide with the full one. The Hamiltonian of mean force formalism, however, is shown to be incompatible with that limit. Physically, the second particle becomes a work source. These theoretical results are illustrated using an exactly solvable harmonic model.
从两个耦合的欠阻尼布朗粒子的随机热力学描述出发，我们展示并比较了三种不同的粗粒化方案，这些方案为两个粒子中的第一个粒子导出了有效的热力学描述：对一个粒子进行边缘化、具有信息流的二分结构以及平均力形式的哈密顿量。在时间尺度分离的极限情况下，即具有快速弛豫时间尺度的第二个粒子相对于第一个缓慢弛豫粒子的坐标局部达到平衡时，第一种和第三种方法得到的有效热力学被证明能够捕捉完整的热力学，并且彼此一致。在二分法中，由于忽略了粒子之间的熵交换，慢部分通常不允许进行精确的热力学描述。从物理上讲，第二个粒子有效地成为了热库的一部分。在第二个粒子变得很重从而具有确定性的极限情况下，前两种粗粒化方法的有效热力学与完整的热力学一致。然而，平均力形式的哈密顿量被证明与该极限不相容。从物理上讲，第二个粒子变成了一个功源。这些理论结果通过一个可精确求解的谐振子模型进行了说明。
