The inference of thermodynamic quantities from the description of an only partially accessible physical system is a central challenge in stochastic thermodynamics. A common approach is coarse-graining, which maps the dynamics of such a system to a reduced effective one. While coarse-graining states of the system into compound ones is a well-studied concept, recent evidence hints at a complementary description by considering observable transitions and waiting times. In this work, we consider waiting time distributions between two consecutive transitions of a partially observable Markov network. We formulate an entropy estimator using their ratios to quantify irreversibility. Depending on the complexity of the underlying network, we formulate criteria to infer whether the entropy estimator recovers the full physical entropy production or whether it just provides a lower bound that improves on established results. This conceptual approach, which is based on the irreversibility of underlying cycles, additionally enables us to derive estimators for the topology of the network, i.e., the presence of a hidden cycle, its number of states, and its driving affinity. Adopting an equivalent semi-Markov description, our results can be condensed into a fluctuation theorem for the corresponding semi-Markov process. This mathematical perspective provides a unifying framework for the entropy estimators considered here and established earlier ones. The crucial role of the correct version of time reversal helps to clarify a recent debate on the meaning of formal versus physical irreversibility. Extensive numerical calculations based on a direct evaluation of waiting time distributions illustrate our exact results and provide an estimate on the quality of the bounds for affinities of hidden cycles.

中文翻译：

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部分可访问马尔可夫网络中的热力学推断：基于转换的等待时间分布的统一视角

从仅部分可访问的物理系统的描述中推断热力学量是随机热力学的核心挑战。一种常见的方法是粗粒度，它将这种系统的动态映射到一个减少的有效系统。虽然系统的粗粒度状态为复合状态是一个经过充分研究的概念，但最近的证据暗示通过考虑可观察的转换和等待时间来进行补充描述。在这项工作中，我们考虑了部分可观察马尔可夫网络的两个连续转换之间的等待时间分布。我们使用它们的比率来制定熵估计器来量化不可逆性。根据底层网络的复杂性，我们制定标准来推断熵估计器是否恢复了完整的物理熵产生，或者它是否只是提供了一个改进既定结果的下限。这种基于底层循环不可逆性的概念方法还使我们能够推导出网络拓扑的估计量，即隐藏循环的存在、状态数和驱动亲和力。采用等价的半马尔可夫描述，我们的结果可以浓缩为对应的半马尔可夫过程的涨落定理。这种数学观点为这里考虑的熵估计器和早期建立的熵估计器提供了一个统一的框架。正确版本的时间逆转的关键作用有助于澄清最近关于形式不可逆性与物理不可逆性含义的辩论。基于对等待时间分布的直接评估的广泛数值计算说明了我们的确切结果，并提供了对隐藏循环亲和性边界质量的估计。