该研究团队表明，与直觉相反，通过忽略部分已经粗粒度的状态空间，可以利用一个名为里程碑的过程的方法，来优化熵产生的估计。研究人员通过多个不同实例的演示，表明里程碑方法能够使得观测结果“更接近潜在的微观动力学”，进而提升了在给定记忆范围内的集总数据的热力学推断精度。他们假设这种优化效果是普遍存在的。
此外，尽管在存在记忆效应的情况下，时间反演的正确的一般物理定义仍然是一个待解之谜，但研究人员通过一系列物理相关的实例，展示了至少对于一阶和二阶的半马尔可夫过程，通常必须摒弃因采用原始马尔可夫时间反演定义而引入的等待时间贡献。
据悉，众多非平衡的活动过程在粗粒度水平下被观测到，这些过程中，各异的微观结构均映射到相同的可观测状态上。这种“集总”式的观测方式展现出了记忆效应，使得在多种情况下，潜在微观动力学的不可逆特性变得模糊难辨，特别是在投影过程掩盖了耗散周期时。因此，观测结果似乎呈现出较低的不可逆性，而要准确推断时间反演对称性的破缺程度则极具挑战性。
附：英文原文
Title: Milestoning estimators of dissipation in systems observed at a coarse resolution
Author: Blom, Kristian, Song, Kevin, Vouga, Etienne, Godec, Aljaz, Makarov, Dmitrii E.
Issue&Volume: 2024-4-16
Abstract: Many nonequilibrium, active processes are observed at a coarse-grained level, where different microscopic configurations are projected onto the same observable state. Such “lumped” observables display memory, and in many cases, the irreversible character of the underlying microscopic dynamics becomes blurred, e.g., when the projection hides dissipative cycles. As a result, the observations appear less irreversible, and it is very challenging to infer the degree of broken time-reversal symmetry. Here we show, contrary to intuition, that by ignoring parts of the already coarse-grained state space we may—via a process called milestoning—improve entropy-production estimates. We present diverse examples where milestoning systematically renders observations “closer to underlying microscopic dynamics” and thereby improves thermodynamic inference from lumped data assuming a given range of memory, and we hypothesize that this effect is quite general. Moreover, whereas the correct general physical definition of time reversal in the presence of memory remains unknown, we here show by means of physically relevant examples that at least for semi-Markov processes of first and second order, waiting-time contributions arising from adopting a naive Markovian definition of time reversal generally must be discarded.
DOI: 10.1073/pnas.2318333121
Source: https://www.pnas.org/doi/abs/10.1073/pnas.2318333121