The celebrated exchange fluctuation theorem—proposed by Jarzynski and Wjcik (2004 Phys. Rev. Lett. 92 230602) for heat exchange between two systems in thermal equilibrium at different temperatures—is explored here for quantum Gaussian states in thermal equilibrium. We employ the Wigner distribution function formalism for quantum states, which exhibits a close resemblance to the classical phase-space trajectory description, to arrive at a formal Jarzynski–Wjcik result. For two Gaussian states in thermal equilibrium at two different temperatures kept in contact with each other for a fixed duration of time, we show that the Jarzynski–Wjcik-like relation reduces to the corresponding classical result in the limit ℏ → 0.

著名的交换波动定理提出的由Jarzynski和Wjcik（2004和物理评论快报。 92 230602），用于在热平衡在不同的两个系统之间的热交换的温度下，在这里探讨了在热平衡量子高斯的状态。我们采用量子态的Wigner分布函数形式主义，与经典的相空间轨迹描述非常相似，得出形式上的Jarzynski-Wjcik结果。对于在两个不同温度下保持固定持续时间彼此接触的两个处于热平衡状态的高斯状态，我们证明了Jarzynski-Wjcik式关系在极限ℏ →0处减小为相应的经典结果。