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摘要翻译：
热定理揭示了平衡态热力学第二定律（即熵的存在），作为哈密顿力学和遍历假设的一般性质的一种表现，它对1和10^{23}$自由度系统有效，对简单和非常复杂的系统有效，反映了微观运动的哈密顿性质。在非平衡态热力学中，具有可比一般性的定理似乎并不存在。然而，即使对简单的混沌系统（即双曲系统）也有可能找到一般的、与模型无关的、对大系统特别感兴趣的性质：混沌假设导致涨落定理，该定理提供了某些非常大的涨落的一般性质，并反映了时间反转对称性。对流体和量子系统的影响作了简要的暗示。讨论了混沌假说、SRB分布和涨落定理的物理意义，并用相空间的粗粒度划分对它们进行了解释和关联。这篇评论是写了一些注意，每个部分和附录是可读的，要么独立于其余部分，要么只有少数交叉引用。
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英文标题：
《Heat and Fluctuations from Order to Chaos》
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作者：
Giovanni Gallavotti
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最新提交年份：
2008
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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：
The Heat theorem reveals the second law of equilibrium Thermodynamics (i.e.existence of Entropy) as a manifestation of a general property of Hamiltonian Mechanics and of the Ergodic Hypothesis, valid for 1 as well as $10^{23}$ degrees of freedom systems, {\it i.e.} for simple as well as very complex systems, and reflecting the Hamiltonian nature of the microscopic motion. In Nonequilibrium Thermodynamics theorems of comparable generality do not seem to be available. Yet it is possible to find general, model independent, properties valid even for simple chaotic systems ({\it i.e.} the hyperbolic ones), which acquire special interest for large systems: the Chaotic Hypothesis leads to the Fluctuation Theorem which provides general properties of certain very large fluctuations and reflects the time-reversal symmetry. Implications on Fluids and Quantum systems are briefly hinted. The physical meaning of the Chaotic Hypothesis, of SRB distributions and of the Fluctuation Theorem is discussed in the context of their interpretation and relevance in terms of Coarse Grained Partitions of phase space. This review is written taking some care that each section and appendix is readable either independently of the rest or with only few cross references.
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PDF链接：
https://arxiv.org/pdf/711.2755
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