Open quantum systems, which are characterized by the exchange of particles, energy, or information with an environment, are ubiquitous in physics and chemistry. Examples range from decoherence in superconducting qubits and charge transport in nanostructures to complex chemical reactions in condensed-phase molecular systems. An accurate theoretical description of their dynamics remains a challenge, particularly in scenarios involving strong system-environment coupling, non-Markovian dynamics, or strong internal many-body interactions.

In this talk, I will discuss our recent work in this area, focusing on the application of the hierarchical equations of motion (HEOM) method. This accurate quantum master equation approach generalizes perturbative schemes by incorporating higher-order contributions and non-Markovian 

memory, thus enabling systematic convergence.  We apply this method to simulate charge and heat transport in molecular nanojunctions. In particular, the important role of electronic-vibrational interaction in these processes is analyzed. Furthermore, the principle of minimal 

dissipation is used to investigate thermodynamic properties in open quantum systems. As a specific example, a quantum Otto cycle within the Anderson impurity model is studied.