The second law of classical equilibrium thermodynamics, based on the positivity of entropy production, asserts that any process occurs only in a direction that some information may be lost (fow out of the system) due to the irreversibility inside the system. However, any thermodynamic system can exhibit fuctuations in which negative entropy production may be observed. In particular, in stochastic quantum processes due to quantum correlations and also memory efects we may see the reversal energy fow (heat fow from the cold system to the hot system) and the backfow of information into the system that leads to the negativity of the entropy production which is an apparent violation of the Second Law. In order to resolve this apparent violation, we will try to properly extend the Second Law to quantum processes by incorporating information explicitly into the Second Law. We will also provide a thermodynamic operational meaning for the fow and backfow of information. Finally, it is shown that negative and positive entropy production can be described by a quantum thermodynamic force
