Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic

Edward Bormashenko

doi:10.3390/e21121150

Abstract

The Landauer principle asserts that “the information is physical”. In its strict meaning, Landauer’s principle states that there is a minimum possible amount of energy required to erase one bit of information, known as the Landauer bound , where T is the temperature of a thermal reservoir used in the process and is Boltzmann’s constant. Modern computers use the binary system in which a number is expressed in the base-2 numeral system. We demonstrate that the Landauer principle remains valid for the physical computing device based on the ternary, and more generally, N-based logic. The energy necessary for erasure of one bit of information (the Landauer bound) remains untouched for the computing devices exploiting a many-valued logic.

Highlights

Modern computers use the binary system, whereby a number is expressed in the base-2 numeral system
The base-2 is ubiquitous in computing devices because of its straightforward implementation in digital electronic circuitry using binary logic gates
Ternary logic based computers based in the “trit” unit of information were successfully developed in Soviet Union by Nicolay Brousentsov [2]

Summary

Introduction

Modern computers use the binary system, whereby a number is expressed in the base-2 numeral system. One of the first computing machines was based on the ternary logic. The present paper does not come into the mathematical details of the ternary (or another) many-valued logics, but extends the Landauer principle to the erasing of the information by the computing machine, based on the many-valued logics. Rolf Landauer, in his papers, argued that “information is physical” and has an energy equivalent [7,8,9] It may be stored in physical systems, such as books and memory chips, and it is transmitted by physical devices exploiting electrical or optical signals [6,7,8]. Principle usually extended to devices that exploit a many-valued logics.

Discussion

Sketch

B Tln2 log log2 33

The of of a memory exploiting a Brownian particle

Conclusions

A Treatiseanalysis on Many-Valued