  It is demonstrated how to construct a Galois connection between two related
systems with entropy. The construction, called the Landauer's connection,
describes coupling between two systems with entropy. It is straightforward and
transfers changes in one system to the other one preserving ordering structure
induced by entropy. The Landauer's connection simplifies the description of the
classical Landauer's principle for computational systems. Categorification and
generalization of the Landauer's principle opens area of modelling of various
systems in presence of entropy in abstract terms.
