孤立量子多体系统及其子系统中的非平衡温度
Temperature Beyond Equilibrium in Isolated Quantum Many-Body Systems and Their Subsystems
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中文总结 AI 辅助
研究孤立量子多体系统及其子系统非平衡态温度，提出温度在正则态族中定位状态的定义，给出非平衡态自然温度定义，逆温度非熵对能量导数，最大熵原理被最小判别信息原理取代，还为子系统发展理论。
中文摘要 AI 辅助
温度是热力学的核心概念之一，但其在非平衡态下的意义仍不明确。在孤立量子多体系统中此问题尤为尖锐，其状态通过幺正演化，不一定接近平衡态且能保持能量相干性，这是经典热力学中没有的特征。非定常量子态包含两种能量涨落。一种与能量占据有关，有通常的热力学解释；另一种源于能量扇区间的相干性并驱动时间依赖性。我们提出，即使在非平衡态下，温度也能在与其能量相干结构兼容的正则态族中定位该状态。这为正则非平衡态给出了自然的温度定义。所得的逆温度一般不是热力学熵关于能量的导数。实际上，最大熵原理通常形式不再适用，而是被最小判别信息原理取代。我们还为子系统发展了相应理论，在子系统中温度一般不能仅从约化态推断，而是由诱导的局部热力学结构决定，在热力学极限下消除了边界模糊性。
英文摘要
Temperature is one of the central concepts of thermodynamics, yet its meaning far from equilibrium remains unclear. The problem is especially challenging in isolated quantum many-body systems, whose states evolve unitarily, may remain far from equilibrium, and retain energy coherence, a genuinely quantum feature with no direct classical counterpart. Specifically, energy fluctuations in a nonstationary quantum state have two distinct origins. Part of them comes from uncertainty in the energy populations and has the usual thermodynamic meaning. The rest comes from quantum coherence between energy sectors and is responsible for the state's time dependence. We propose that, even away from equilibrium, temperature identifies the state within the family of regular states sharing the same energy-coherence structure. This provides a natural definition of temperature for a broad class of nonequilibrium quantum states. The resulting inverse temperature is not, in general, obtained by differentiating entropy with respect to energy. The usual maximum-entropy principle is instead replaced by a principle of minimum discrimination information, which selects the least distinguishable state compatible with the prescribed energy and coherence structure. We also extend the construction to subsystems and show that, although their inverse temperature is not determined by the reduced state alone, its instantaneous rate of change is a local quantity, determined by the thermodynamic structure induced on the subsystem at that time.
