# Landauer’s Principle as a Special Case of Galois Connection

@article{Kycia2018LandauersPA,
title={Landauer’s Principle as a Special Case of Galois Connection},
journal={Entropy},
year={2018},
volume={20}
}
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…

## Figures and Tables from this paper

• Physics
ArXiv
• 2020
Using recent results on the Landauer's bound in multivalued logic, the difficulties and pitfalls of how to apply this principle are discussed, using Szilard's version of Maxwell's demon experiment and use of equilibrium Thermodynamics.
• Physics
• 2020
Abstract We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models.
• Physics
Technical Transactions
• 2020
Abstract We discuss, using recent results on the thermodynamics of multivalued logic, the difficulties and pitfalls of how to apply the Landauer’s principle to thermodynamic computer memory models.
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
• Physics
• 2020
This is an overview article that contains the discussion of the connection between information and physics at the elementary level. We present a derivation of Landauer’s bound for heat emission
• Computer Science
IPMU
• 2020
This paper surveys recent results obtained in the construction of Galois connections between unbalanced structures, focusing specially on fuzzy structures that have been considered so far: fuzzy preposets, fuzzy preordered structures, and fuzzy T-digraphs.
• Physics
Entropy
• 2021
This work treated hydrophobic interactions responsible for the self-assembly of viruses as an information-processing mechanism and showed a similarity of these submicron-scale processes with theSelf-assembly in colloidal crystals, droplet clusters, and liquid marbles.
• Computer Science
Mathematical Methods in the Applied Sciences
• 2020
Fuzzy‐directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in
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
The informational re-interpretation of the basic laws of the mechanics exploiting the Landauer principle is suggested: the informational content of the inertial and gravitational masses is the same.

## References

SHOWING 1-10 OF 48 REFERENCES

• J. Boyling
• Mathematics
Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
• 1972
Carathéodory’s formulation of classical thermodynamics is cast into a mathematically rigorous form, in which such well-known results as the existence of entropy and of (positive) absolute
• Physics
Nature
• 2012
It is established that the mean dissipated heat saturates at the Landauer bound in the limit of long erasure cycles, demonstrating the intimate link between information theory and thermodynamics and highlighting the ultimate physical limit of irreversible computation.
• Physics
Physical review letters
• 2018
This experimental investigation substantiates an intimate link between information thermodynamics and quantum candidate systems for information processing and demonstrates a quantum version of the Landauer principle, i.e., an equality associated with the energy cost of information erasure in conjunction with the entropy change of the associated quantized environment.
This article sums up a stage of the development of the relationship between category theory and proof theory and shows how already in 1967 category theory had made explicit a number of conceptual advances that were entering into the everyday practice of mathematics.
• Mathematics, Computer Science
ArXiv
• 2014
Any convex linear, lower semicontinuous functor from FinStat to the additive monoid $[0,\infty]$ which vanishes when s is optimal must be a scalar multiple of this relative entropy.
• Physics
• 1998