论文标题
数量古典波动关系和热力学的第二定律：量子线性振荡器
Quantal-classical fluctuation relation and the second law of thermodynamics: The quantum linear oscillator
论文作者
论文摘要
在这项工作中，我们研究了在量子线性振荡器内部驱动的波动关系和热力学的第二定律。为了超越标准方法（两点投影测量1），并在单个基础上渲染在量子和经典域中讨论的，我们根据wigner函数及其在相位空间（x，p）中对此标准方法进行了重新铸造。借助从（x，p）到角度坐标（ϕ，i）的规范转换，然后我们可以在Wigner表示中得出Crooks波动关系的无测量（经典）形式。这使我们能够介绍W_ {i_0，I_ {tau}}的工作，该工作与（I_0）到（I_ {tau}）在TAU期间与（I_0）运行相关联，这是对热力学工作的量子概括，其根部与其根源在经典热力学中。该量子工作不同于能量差E_ {I_0，I_ {tau}} = E（I_ {tau}） - E（i_0），除非beta，hbar，hbar--> 0。因此，我们将获得量子级别的不平等不平等delta f_ {beta f_ {beta} {beta} {beta} \ leq leq <w> pe _ p} p p}其中p，delta f_ {beta}和<w> _p分别表示工作（quasi） - 概率分布，自由能差和平均工作，分别与内部能量差delta u区分开来，而<w> _p _p-> _p-> delta u在beta，beta，hbar，hbar，hbar-> 0中的限制。因此，我们还可以引入量子热q_q = delta u -w，即使是由于其中的量子波动而导致的热隔离系统。这是比从标准方法获得的<w> _p = delta u更细粒度的结果。由于热力学工作的无测量性质w_ {i_0，i_ {tau}}，我们的结果也可以应用于（非热）初始状态rho_0 =（1-gamma）rho_ {beta} + gamma sigma sigma sigma sigma sigma sigma \ ne rho_ \ ne rho_ {beta}。
In this work, we study the fluctuation relation and the second law of thermodynamics within a quantum linear oscillator externally driven over the period of time t = tau. To go beyond the standard approach (the two-point projective measurement one) to this subject and also render it discussed in both quantum and classical domains on the single footing, we recast this standard approach in terms of the Wigner function and its propagator in the phase space (x,p). With the help of the canonical transformation from (x,p) to the angle-action coordinates (ϕ,I), we can then derive a measurement-free (classical-like) form of the Crooks fluctuation relation in the Wigner representation. This enables us to introduce the work W_{I_0,I_{tau}} associated with a single run from (I_0) to (I_{tau}) over the period tau, which is a quantum generalization of the thermodynamic work with its roots in the classical thermodynamics. This quantum work differs from the energy difference e_{I_0,I_{tau}} = e(I_{tau}) - e(I_0) unless beta, hbar --> 0. Consequently, we will obtain the quantum second-law inequality Delta F_{beta} \leq <W>_{P} \leq <e>_{P} = Delta U, where P, Delta F_{beta}, and <W>_P denote the work (quasi)-probability distribution, the free energy difference, and the average work distinguished from the internal energy difference Delta U, respectively, while <W>_P --> Delta U in the limit of beta, hbar --> 0 only. Therefore, we can also introduce the quantum heat Q_q = Delta U - W even for a thermally isolated system, resulting from the quantum fluctuation therein. This is a more fine-grained result than <W>_P = Delta U obtained from the standard approach. Owing to the measurement-free nature of the thermodynamic work W_{I_0,I_{tau}}, our result can also apply to the (non-thermal) initial states rho_0 = (1-gamma) rho_{beta} + gamma sigma with sigma \ne rho_{beta}.
