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摘要翻译：
计算了非平衡Markovian系综的熵变：（1）系综相密度$p(t)$迭代映射，$p(t)=\mathbb{M}(t)p(t-\delta)$在详细平衡转移矩阵$\mathbb{M}(t)$下，(2)不变相密度$\pi(t)=\mathbb{M}(t)^{\infty}\pi(t)$。采用变分熵为零的虚拟测量协议，得到了不可逆熵变的Jeffreys测度的精确表达式$\Mathcal{J}(t)=\sum_{\gamma}[p(t)-\pi(t)]\ln\bfrac{p(t)}{\pi(t)}$和可逆熵变的Kullbach-Leibler测度的精确表达式$\Mathcal{D}_{KL}(t)=\sum_{\gamma}\pi(0)\ln\bfrac{\pi(0)}{\pi(t)}$。讨论了$\Mathcal{J}$的五个性质，导出了Clausius定理。
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英文标题：
《Equality statements for entropy change in open systems》
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作者：
John M. Robinson
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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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一级分类：Physics 物理学
二级分类：Soft Condensed Matter 软凝聚态物质
分类描述：Membranes, polymers, liquid crystals, glasses, colloids, granular matter
膜，聚合物，液晶，玻璃，胶体，颗粒物质
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英文摘要：
The entropy change of a (non-equilibrium) Markovian ensemble is calculated from (1) the ensemble phase density $p(t)$ evolved as iterative map, $p(t) = \mathbb{M}(t) p(t- \Delta t)$ under detail balanced transition matrix $\mathbb{M}(t)$, and (2) the invariant phase density $\pi(t) = \mathbb{M}(t)^{\infty} \pi(t) $. A virtual measurement protocol is employed, where variational entropy is zero, generating exact expressions for irreversible entropy change in terms of the Jeffreys measure, $\mathcal{J}(t) = \sum_{\Gamma} [p(t) - \pi(t)] \ln \bfrac{p(t)}{\pi(t)}$, and for reversible entropy change in terms of the Kullbach-Leibler measure, $\mathcal{D}_{KL}(t) = \sum_{\Gamma} \pi(0) \ln \bfrac{\pi(0)}{\pi(t)}$. Five properties of $\mathcal{J}$ are discussed, and Clausius' theorem is derived.
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PDF链接：
https://arxiv.org/pdf/711.4957
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