Landauer's principle as a special case of Galois connection

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.Comment: 24 pages, 3 figure

Inverse problem in the calculus of variations -- functional and antiexact forms

We connect the well-known theory of functional forms with the (local) theory of antiexact differential forms. That allows reinterpreting the notions from the inverse problem of the calculus of variations in a new light. The connection between antiexact forms and the obstruction to the equation to being variational is provided. The condition for the existence of a variational multiplier is given. The most important result of the paper is to formulate, in terms of antiexact forms, the variational problem for some differential equations that are not variational and neither have a multiplier.Comment: 13 page

Entropy in Thermodynamics: from Foliation to Categorization

summary:We overview the notion of entropy in thermodynamics. We start from the smooth case using differential forms on the manifold, which is the natural language for thermodynamics. Then the axiomatic definition of entropy as ordering on a set that is induced by adiabatic processes will be outlined. Finally, the viewpoint of category theory is provided, which reinterprets the ordering structure as a category of pre-ordered sets