Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig (MZ) projection operator formalism, which is one of the most important methods of modern nonequilibrium statistical mechanics, allows for a systematic derivation of irreversible transport equations from reversible microdynamics and thus provides a useful framework for understanding this issue. However, discussions of the MZ formalism in philosophy of physics tend to focus on simple variants rather than on the more sophisticated ones used in modern physical research. In this work, I will close this gap by studying the problems of probability and irreversibility using the example of Grabert’s time-dependent projection operator formalism. This allows to better understand how general proposals for understanding probability in statistical mechanics, namely (a) quantum approaches and (b) almost-objective probabilities, can be accomodated in the MZ formalism. Moreover, I will provide a detailed physical analysis, based on the MZ formalism, of various proposals from the philosophical literature, such as (a) Robertson’s theory of justifying coarse-graining via autonomous macrodynamics, (b) Myrvold’s problem of explaining autonomous macrodynamics, and (c) Wallace’s simple dynamical conjecture.

从时间可逆确定性微观动力学解释随机不可逆宏观动力学的出现是物理学哲学中的关键问题之一。Mori-Zwanzig (MZ) 投影算子形式是现代非平衡统计力学中最重要的方法之一，它允许从可逆微动力学系统推导不可逆输运方程，从而为理解这个问题提供了一个有用的框架。然而，物理学哲学中对 MZ 形式主义的讨论倾向于关注简单的变体，而不是现代物理研究中使用的更复杂的变体。在这项工作中，我将通过使用 Grabert 的时间相关投影算子形式主义的例子研究概率和不可逆性问题来弥补这一差距。这有助于更好地理解理解统计力学中概率的一般建议，即 (a) 量子方法和 (b) 几乎客观的概率，如何适应 MZ 形式主义。此外，我将基于 MZ 形式对哲学文献中的各种建议进行详细的物理分析，例如（a）罗伯逊通过自主宏观动力学证明粗粒度的理论，（b）米尔沃尔德解释自主宏观动力学的问题， (c) 华莱士的简单动力猜想。