Approach to equilibrium in open quantum statistical mechanics under detailed balance condition

In this paper, we study the long-time behavior of a quantum dynamical semigroup on a general C*-algebra under the quantum detailed balance condition of [Kossakowski et al., Commun. Math. Phys. 57, 97 (1977)], in which the connection between this detailed balance condition and Kubo–Martin–Schwinger (KMS) condition was investigated. Moreover, this work provides a natural extension to our recent results of [Ouyang and Sigal, arXiv:2503.13376 (2025)], where we studied long-time behavior of Markovian open quantum systems, governed by von Neumann–Lindblad equation, under the detailed balance condition. In this paper, we establish criteria for ergodicity and the property of returning to equilibrium for a quantum dynamical system by using techniques from spectral theory and scattering theory.