  An important step to incorporate information in the second law of
thermodynamics was done by Landauer, showing that the erasure of information
implies an increase in heat. Most attempts to justify Landauer's erasure
principle are based on thermodynamic argumentations. Here, using just the
time-reversibility of classical microscopic laws, we identify three types of
the Landauer's erasure principle depending on the relation between the two
final environments: the one linked to a logical input 1 and the other to the
logical input 0. The strong type (which is the original Landauer's formulation)
requires the final environments to be in thermal equilibrium. The intermediate
type giving the entropy change of $k_B \ln 2$ occurs when the two final
environments are identical macroscopic states. Finally, the weak Landauer's
principle, providing information erasure with no entropy change, when the two
final environments are macroscopically different. Even though the above results
are formally valid for classical erasure gates, a discussion on their natural
extension to quantum scenarios is presented. This paper strongly suggests that
the original Landauer's principle (based on the assumption of thermalized
environments) is fully reasonable for microelectronics, but it becomes less
reasonable for future few-atoms devices working at THz frequencies. Thus, the
weak and intermediate Landauer's principles, where the erasure of information
is not necessarily linked to heat dissipation, are worth investigating.
