We present a Gedankenexperiment that leads to a violation of detailed balance if quantum mechanical transition probabilities are treated in the usual way by applying Fermi's "golden rule". This Gedankenexperiment introduces a collection of two-level systems that absorb and emit radiation randomly through non-reciprocal coupling to a waveguide, as realized in specific chiral quantum optical systems. The non-reciprocal coupling is modeled by a hermitean Hamiltonian and is compatible with the time-reversal invariance of unitary quantum dynamics. Surprisingly, the combination of non-reciprocity with probabilistic radiation processes entails negative entropy production. Although the considered system appears to fulfill all conditions for Markovian stochastic dynamics, such a dynamics violates the Clausius inequality, a formulation of the second law of thermodynamics. Several implications concerning the interpretation of the quantum mechanical formalism are discussed.

中文翻译：

---

费米黄金法则和热力学第二定律

如果通过应用费米的“黄金法则”以通常的方式处理量子力学跃迁概率，我们提出了一个 Gedanken 实验，该实验会导致违反详细平衡。该 Gedanken 实验介绍了一组两能级系统，这些系统通过与波导的非互易耦合随机吸收和发射辐射，如在特定手性量子光学系统中实现的那样。非互易耦合由厄米哈密顿量建模，并且与幺正量子动力学的时间反转不变性兼容。令人惊讶的是，非互易性与概率辐射过程的结合需要产生负熵。尽管所考虑的系统似乎满足马尔可夫随机动力学的所有条件，但这种动力学违反了克劳修斯不等式，热力学第二定律的表述。讨论了有关量子力学形式主义解释的几个含义。