We derive a semiclassical nonequilibrium work identity by applying the Wigner–Weyl quantization scheme to the Jarzynski identity for a classical Hamiltonian. This allows us to extend the concept of work to the leading order in ℏ . We propose a geometric interpretation of this semiclassical Jarzynski relation in terms of trajectories in a complex phase space and illustrate it with the exactly solvable case of the quantum harmonic oscillator.

中文翻译：

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Weyl表示中的半经典功和量子功身份

通过将Wigner-Weyl量化方案应用于经典哈密顿量的Jarzynski身份，我们得出了半经典的非平衡功身份。这使我们可以将工作概念扩展到ℏ中的领先顺序。我们根据复杂相空间中的轨迹提出了这种半经典Jarzynski关系的几何解释，并用量子谐波振荡器的精确可解情况对其进行了说明。