标题： 扩展的结构动力学——从可逆动力学中产生的不可逆性 显示英文标题

标题： Extended Structural Dynamics -- Emergent Irreversibility from Reversible Dynamics

摘要： 孤立的确定性系统中不可逆性的出现仍然是统计力学基础中的一个核心问题。传统的方法，如玻尔兹曼的H定理和兰道尔对玻尔兹曼方程的推导，依赖于概率假设，并且仅限于稀薄气体和短时间尺度。在本工作中，我们引入了扩展结构动力学（ESD），这是一个确定性框架，其中不可逆性来源于结构粒子的内部几何结构。在ESD中，粒子具有有限大小和内部自由度，如旋转和振动，这些自由度与平动运动动态耦合。这种耦合在扩展相空间中引发了不稳定性、非线性反馈和混沌混合，即使在时间反演对称定律下也是如此。我们证明了平衡态指数地主导了相空间的可访问体积，而受约束的构型（例如纯旋转）形成了测度为零的子集。这提供了一种熵增长的几何推导，逆转概率按Prev抑制，而重现时间按Trec缩放。这些结果在不进行粗粒化、随机性或微调的情况下解决了洛施密特和策梅洛悖论。我们进一步将模型扩展到带电系统（cESD），其中长程电磁相互作用驱动连续的结构耦合。因此，ESD为涌现的热力学行为提供了一个确定性和可检验的机制，其应用范围从介观系统到宇宙学的时间箭头。 显示英文摘要

摘要： The emergence of irreversibility in isolated, deterministic systems remains a central problem in the foundations of statistical mechanics. Traditional approaches, such as Boltzmann's H-theorem and Lanford's derivation of the Boltzmann equation, rely on probabilistic assumptions and are constrained to dilute gases and short timescales. In this work, we introduce Extended Structural Dynamics (ESD), a deterministic framework in which irreversibility arises from the internal geometry of structured particles. In ESD, particles possess finite size and internal degrees of freedom, such as rotation and vibration, that are dynamically coupled to translational motion. This coupling induces instability, nonlinear feedback, and chaotic mixing in the extended phase space, even under time-reversal symmetric laws. We show that equilibrium states exponentially dominate the accessible volume of phase space, while constrained configurations (e.g., pure rotation) form measure-zero subsets. This yields a geometric derivation of entropy growth, with reversal probabilities suppressed as Prev and recurrence times scaling as Trec. These results address the Loschmidt and Zermelo paradoxes without coarse-graining, randomness, or fine-tuning. We further extend the model to charged systems (cESD), where long-range electromagnetic interactions drive continuous structural coupling. ESD thus provides a deterministic and testable mechanism for emergent thermodynamic behavior, with applications ranging from mesoscopic systems to the cosmological arrow of time.