The entropy production rate is a key quantity in nonequilibrium thermodynamics of both classical and quantum processes. No universal theory of entropy production is available to date, which hinders progress toward its full grasping. By using a phase space-based approach, here we take the current framework for the assessment of thermodynamic irreversibility all the way to quantum regimes by characterizing entropy production—and its rate—resulting from the continuous monitoring of a Gaussian system. This allows us to formulate a sharpened second law of thermodynamics that accounts for the measurement back action and information gain from a continuously monitored system. We illustrate our framework in a series of physically relevant examples.

熵生产率是经典过程和量子过程的非平衡热力学中的关键量。迄今为止，尚无通用的熵产生理论，这阻碍了它的全面掌握。通过使用基于相空间的方法，这里我们采用当前框架，通过对熵产生及其速率进行表征，来评估热力学不可逆性，直至量子态，该熵是由对高斯系统的连续监测得出的。这使我们能够制定更清晰的热力学第二定律，该定律考虑了测量反作用和来自连续监控系统的信息增益。我们通过一系列与物理相关的示例来说明我们的框架。