如何定义非平衡量子自旋系统的熵产生？

非平衡态热力学中的最大熵原理：简史及Wolfgang Dreyer的贡献

The Maximum Entropy Principle in Nonequilibrium Thermodynamics: A Brief History and the Contributions of Wolfgang Dreyer

本文回顾了最大熵原理作为Boltzmann方程矩封闭的简史，并重点探讨了Wolfgang Dreyer在经典与相对论框架下的两篇基础性论文对该原理的应用及其与Rational Extended Thermodynamics宏观理论的比较。

相对熵：与平衡涨落和非平衡偏差有关的自由能

Relative Entropy: Free Energy Associated with Equilibrium Fluctuations and Nonequilibrium Deviations

以水溶液中的一维大分子为例，我们证明了信息论中的相对熵$\sum_k p_k\ln(p_k/p_k^*)$在单分子平衡和非平衡构象涨落的能量学中具有天然的作用。它被认为是平衡态下与密度涨落有关的自由能差，而在非平衡态弛豫中则与偏离平衡态的分布有关。这一结果可以推广到任何其他等温大分子体系，同时也为著名的数学结果提供了有趣的物理解释。

量子分析与非平衡响应

Quantum Analysis and Nonequilibrium Response

导出了在量子统计物理中起基础作用的$e^{-A}, A^{-1}$和$\log A$的量子导数，并证明了它们在Hilbert空间中无界正算子$A$的收敛性.利用基于这些量子导数的量子分析，导出了非平衡系统中熵算符的基本方程，并将Zubarev理论推广到关于微扰的无限阶.利用熵算子的一般微扰展开式的一阶项，Kubo的线性响应被重新推导并表示为相关哈密顿量${\cal H}$的内导数$δ_{\cal H}$。对$σ(ω)$的电导率进行了讨论。

Nonequilibrium Entropy in an Extended State Space

This chapter deals with our recent attempt to extend the notion of equilibrium (EQ) entropy to nonequilibrium (NEQ) systems so that it can also capture memory effects. This is done by enlarging the equilibrium state space by introducing internal variables. These variables capture the irreversibility due to internal processes. By a proper choice of the enlarged state space, the entropy becomes a state function, which shares many properties of the EQ entropy, except for a nonzero irreversible entropy generation. We give both a thermodynamic and statistical extension of the entropy and prove thei…

Exact equalities and thermodynamic relations for nonequilibrium steady states

We study thermodynamic operations which bring a nonequilibrium steady state (NESS) to another NESS in physical systems under nonequilibrium conditions. We model the system by a suitable Markov jump process, and treat thermodynamic operations as protocols according to which the external agent varies parameters of the Markov process. Then we prove, among other relations, a NESS version of the Jarzynski equality and the extended Clausius relation. The latter can be a starting point of thermodynamics for NESS. We also find that the corresponding nonequilibrium entropy has a microscopic representat…

非平衡经典热力学中熵与热力学温度作为Hahn-Banach定理直接推论的研究：I. 存在性

Entropy and Thermodynamic Temperature in Nonequilibrium Classical Thermodynamics as Immediate Consequences of the Hahn-Banach Theorem: I. Existence

该研究从热力学第二定律的Kelvin-Planck表述出发，借助Hahn-Banach定理直接证明非平衡态下局部比熵与热力学温度状态函数的存在性，无需限定平衡态条件，相关性质将在配套论文展开。