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

## Abstract

**:**

## 1. Introduction

## 2. Discussion

_{1}and undergoes a reversible isothermal expansion, which doubles its available volume [21]. Note, that the particle initially occupies the left side of the cylinder. Heat k

_{B}T

_{1}ln2 is drawn from the bath and work ${k}_{B}{T}_{1}ln2$ is extracted. This process is equivalent to the removal of the partition at the midpoint of the cylinder, thus, one bit of information is erased, if one bit finds particle m at a certain side (left in our case) of the cylinder, as shown in Figure 2 [10]. Thus, heat k

_{B}T

_{1}ln2 spent by the thermal bath was exploited for erasure of 1 bit of information.

_{1}is disconnected from the engine at this stage). At the next stage, the engine is connected to the thermal bath T

_{2}and exerted to the reversible isothermal compression. A piston reversibly and isothermally compresses the space occupied by the particle m from full to half volume. One bit of information is recorded by the engine. Heat ${Q}_{2}=$ k

_{B}T

_{2}ln2, is delivered to the heat bath, and work kT

_{2}ln2 is consumed. At the last stage of the cycle the engine is disconnected from the reservoir T

_{2}and the system is adiabatically heated to the temperature T

_{1}. No entropy and informational changes take place at this stage. The work of the minimal Carnot engine illustrates the Landauer principle: Recording/erasing one bit of information demands ${k}_{B}Tln2$ units of energy.

_{2}3 bits of information [29]. Thus, an energy bound for erasing of one bit of information for the ternary computers equals:

## 3. Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Finding of the particle M in the certain (left or right) half of the chamber corresponds to the recording of 1 bit of information.

**Figure 2.**Sketch of the minimal single-particle thermal machine is depicted. Particle M moves the piston. The machine works between the hot (T

_{1}) and cold (T

_{2}) thermal reservoirs which may be finite. The conditions of “thermalization” (randomization) of the particle motion are discussed.

**Figure 3.**The qubit model of a memory exploiting a Brownian particle M in a symmetrical double-well potential with position y which can be stably trapped in either left or right well, corresponding to informational states $m=0;m=1$ (see Reference [9]).

**Figure 4.**Finding of the particle m in the certain one-third part of the chamber corresponds to the recording of 1 bit of information. Thus, the “trit”-based computation becomes possible.

**Figure 5.**The trit-based model of a memory exploiting a Brownian particle M in a symmetrical triple-well potential with position y which can be stably trapped in either central, left or right well, corresponding to the informational states, namely: $m=-1;m=0;m=1$.

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**MDPI and ACS Style**

Bormashenko, E. Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic. *Entropy* **2019**, *21*, 1150.
https://doi.org/10.3390/e21121150

**AMA Style**

Bormashenko E. Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic. *Entropy*. 2019; 21(12):1150.
https://doi.org/10.3390/e21121150

**Chicago/Turabian Style**

Bormashenko, Edward. 2019. "Generalization of the Landauer Principle for Computing Devices Based on Many-Valued Logic" *Entropy* 21, no. 12: 1150.
https://doi.org/10.3390/e21121150