The second law of thermodynamics points to the existence of an ‘arrow of time’, along which entropy only increases. This arises despite the time-reversal symmetry (TRS) of the microscopic laws of nature. Within quantum theory, TRS underpins many interesting phenomena, most notably topological insulators^1,2,3,4 and the Haldane phase of quantum magnets^5,6. Here, we demonstrate that such TRS-protected effects are fundamentally unstable against coupling to an environment. Irrespective of the microscopic symmetries, interactions between a quantum system and its surroundings facilitate processes that would be forbidden by TRS in an isolated system. This leads not only to entanglement entropy production and the emergence of macroscopic irreversibility^7,8,9, but also to the demise of TRS-protected phenomena, including those associated with certain symmetry-protected topological phases. Our results highlight the enigmatic nature of TRS in quantum mechanics and elucidate potential challenges in utilizing topological systems for quantum technologies.

热力学第二定律指出了“时间箭头”的存在，沿此时间熵仅增加。尽管存在微观自然定律的时间反转对称性（TRS），但仍会出现这种情况。在量子理论内，TRS支持许多有趣的现象，最著名的是拓扑绝缘体^1,2,3,4和量子磁体^5,6的Haldane相。在这里，我们证明了这种受TRS保护的效应在与环境耦合方面从根本上是不稳定的。不论微观对称性如何，量子系统与其周围环境之间的相互作用都有助于在隔离系统中TRS禁止的过程。这不仅导致纠缠熵的产生和宏观不可逆性的出现^7,8,9，也消除了受TRS保护的现象，包括与某些对称保护的拓扑阶段相关的现象的消亡。我们的研究结果凸显了TRS在量子力学中的神秘本质，并阐明了将拓扑系统用于量子技术的潜在挑战。