Quantum speed limit time in thermodynamic contexts: Linking CPTP dynamics and repetitive interaction

In this paper, we examine thermodynamically driven dissipative processes that lead to an active thermodynamic equilibrium system. These processes are modeled using a quantum collision framework, in which the dissipative contribution is explicitly derived via jump operators. The system under consideration involves either a single qubit or two qubits. In both cases, the system under consideration undergoes repeated interactions with a composed environment of a set of independent ancillas. Hence, by performing a truncated series expansion of the unitary operator, we derive an effective master equation that captures the dissipative effects. Then, our study explores the relationship between quantum speed limit time and various thermodynamic and geometric quantities, particularly in the context of quantum battery charging. The results are interpreted physically by highlighting the impact of repeated interactions on the system's behavior and its evolution toward a stationary regime characterized by active thermodynamic equilibrium.