Differential Landauer's principle

Landauer's principle states that the erasure of information must be a dissipative process. In this paper, we carefully analyze the recording and erasure of information on a physical memory. On the one hand, we show that, in order to record some information, the memory has to be driven out of equilibrium. On the other hand, we derive a differential version of Landauer's principle: We link the rate at which entropy is produced at every time of the erasure process to the rate at which information is erased.