热力学第二定律作为量子自旋系统的确定性定理

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Reviews in Mathematical Physics Pub Date : 2021-12-02 DOI:10.1142/s0129055x22300059

W. Wreszinski

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引用次数: 1

摘要

我们回顾了热力学第二定律作为一个定理的方法，该定理证明了一类经历自同构（酉）绝热变换的量子自旋系统的平均（吉布斯-冯-诺依曼）熵的增长。与环境的非自同构相互作用，尽管已知平均会产生具有有限自由度的系统的熵的严格减少，但被证明平均保持平均熵。结果主要取决于平均熵的两个性质，经典系统的Robinson和Ruelle以及量子晶格系统的Lanford和Robinson证明了这两个性质：上半连续性和有效性。

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The second law of thermodynamics as a deterministic theorem for quantum spin systems

We review our approach to the second law of thermodynamics as a theorem assering the growth of the mean (Gibbs-von Neumann) entropy of a class of quantum spin systems undergoing automorphic (unitary) adiabatic transformations. Non-automorphic interactions with the environment, although known to produce on the average a strict reduction of the entropy of systems with ﬁnite number of degrees of freedom, are proved to conserve the mean entropy on the average. The results depend crucially on two properties of the mean entropy, proved by Robinson and Ruelle for classical systems, and Lanford and Robinson for quantum lattice systems: upper semicontinuity and aﬃnity.

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来源期刊

Reviews in Mathematical Physics 物理-物理：数学物理

CiteScore

3.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Reviews in Mathematical Physics fills the need for a review journal in the field, but also accepts original research papers of high quality. The review papers - introductory and survey papers - are of relevance not only to mathematical physicists, but also to mathematicians and theoretical physicists interested in interdisciplinary topics. Original research papers are not subject to page limitations provided they are of importance to this readership. It is desirable that such papers have an expository part understandable to a wider readership than experts. Papers with the character of a scientific letter are usually not suitable for RMP.