Quantum Speed Limit for the Information Processing of Quantum Thermodynamical Systems

We first generalize the second law of thermodynamics involving the information processing in the autonomous quantum Hamiltonian systems including the system, heat bath, work reservoir and memory in more generic scenario, where the system, bath and memory are initially correlated. We demonstrate that the work reservoir plays a role as a catalyst and characterize the corresponding thermal operation. Then, we define an effective quantum speed limit, which we call quantum thermodynamic speed limit. We derive its relation to the Landauer's bound and explore its operation meaning in terms of the quantum hypothesis testing