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摘要翻译：
考虑一个由慢子系统S和快子系统F组成的哈密顿系统，S的自治动力学是由有效哈密顿量驱动的，但它的热力学是出乎意料的。我们证明，当S到F之间存在一个明确的因果箭头时，对于S会出现一个明确的热力学时间箭头（第二定律），并且反作用可以忽略不计。这是因为F对S的反作用是由违反刘维尔定理的非全局哈密顿Born-Oppenheimer项描述的，使得第二定律不适用于S。如果S和F是混合的，在因果箭头条件下，它们用微正则分布P(S)和P(SF)来描述。它们的结构支持最近在机器学习中提出的因果推理原理。
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英文标题：
《Relating the thermodynamic arrow of time to the causal arrow》
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作者：
Armen E. Allahverdyan and Dominik Janzing
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最新提交年份：
2007
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分类信息：
一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
Consider a Hamiltonian system that consists of a slow subsystem S and a fast subsystem F. The autonomous dynamics of S is driven by an effective Hamiltonian, but its thermodynamics is unexpected. We show that a well-defined thermodynamic arrow of time (second law) emerges for S whenever there is a well-defined causal arrow from S to F and the back-action is negligible. This is because the back-action of F on S is described by a non-globally Hamiltonian Born-Oppenheimer term that violates the Liouville theorem, and makes the second law inapplicable to S. If S and F are mixing, under the causal arrow condition they are described by microcanonic distributions P(S) and P(S|F). Their structure supports a causal inference principle proposed recently in machine learning.
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PDF链接：
https://arxiv.org/pdf/708.1175
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