Landauer's principle as a special case of Galois connection

TL;DR

This paper introduces the Landauer's connection, a Galois connection framework that models entropy-based coupling between systems, simplifying and generalizing Landauer's principle for broader applications.

Contribution

It constructs a Galois connection called the Landauer's connection to model entropy coupling, providing a categorical and generalized perspective on Landauer's principle.

Findings

Provides a new categorical framework for entropy interactions

Simplifies classical Landauer's principle description

Opens avenues for modeling entropy in diverse systems

Abstract

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.