论文标题
在系统 - 环境纯状态下的量子熵和过量的熵产生
On Quantum Entropy and Excess Entropy Production in a System-Environment Pure State
论文作者
论文摘要
我们探索了一个最近引入的量子热力学熵$ s^q_ {univ} $的复合系统 - 环境计算“宇宙”的纯状态,并带有简单的系统$ \ MATHCAL {s} $耦合到恒温浴$ \ Mathcal $ \ Mathcal {e} $。主要重点是“熵过多”,其中量子熵变化比经典无熵能量关系所预期的要大。我们通过时间依赖状态的量子扩散及其与微炮壳的概念进行分析。熵采用基础依赖的香农信息定义。我们主张零级$ \ mathcal {se} $能量基础作为独特的选择,它在弱耦合和高密度的限制中提供了经典的热力学关系,包括精确的系统和环境组件。熵生产是由于两种过程而进行的。第一个是经典的“构造”,它填充了微域内壳中状态的全密度。第二个是与波袋的量子扩散或“量子构造”相关的过量熵产生,从而有效地增加了能量壳的宽度。具有有限的微炮壳宽度的Lorentzian叠加导致经典结果作为限制情况,没有过多的熵。然后,我们将单个$ \ MATHCAL {SE} $零定位状态视为极端熵生产的检查项目。对于时间依赖性洛伦兹叠加和计算验证的统一处理,可以获得系统的形式结果。据推测,自由能的想法可能会扩展到与多余熵产生相对应的“可用能量”的概念。因此,从经典限制到极端量子条件的量子热力学熵的统一视角。
We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$. The principal focus is "excess entropy production" in which the quantum entropy change is greater than expected from the classical entropy-free energy relationship. We analyze this in terms of quantum spreading of time dependent states, and its interplay with the idea of a microcanonical shell. The entropy takes a basis-dependent Shannon information definition. We argue for the zero-order $\mathcal{SE}$ energy basis as the unique choice that gives classical thermodynamic relations in the limit of weak coupling and high density of states, including an exact division into system and environment components. Entropy production takes place due to two kinds of processes. The first is classical "ergodization" that fills the full density of states within the microcanonical shell. The second is excess entropy production related to quantum spreading or "quantum ergodization" of the wavepacket that effectively increases the width of the energy shell. Lorentzian superpositions with finite microcanonical shell width lead to classical results as the limiting case, with no excess entropy. We then consider a single $\mathcal{SE}$ zero-order initial state, as the examplar of extreme excess entropy production. Systematic formal results are obtained for a unified treatment of excess entropy production for time-dependent Lorentzian superpositions, and verified computationally. It is speculated that the idea of free energy might be extended to a notion of "available energy" corresponding to the excess entropy production. A unified perspective on quantum thermodynamic entropy is thereby attained from the classical limit to extreme quantum conditions.