Abstract
Understanding the mixing of open quantum systems is a fundamental problem in physics and quantum information science. Existing approaches for estimating the mixing time often rely on the spectral gap estimation of the Lindbladian generator, which is typically assumed to satisfy detailed balance conditions. However, in practice, estimating this gap of the full Lindbladian can be challenging, even when both the Hamiltonian and dissipative parts of the system are relatively simple. We propose a novel theoretical framework to estimate the mixing time of open quantum systems that treats the Hamiltonian and dissipative parts separately, thus circumventing the need for a priori estimation of the spectral gap of the full Lindbladian generator. Our approach also does not assume the full Lindbladian to be detailed balanced. The technique is based on the construction of an energy functional inspired by the hypocoercivity of (classical) kinetic theory.