# General Formula for the Efficiency of Quantum-Mechanical Analog of the Carnot Engine

## Abstract

**:**

## 1. Introduction

## 2. Derivation of the General Formula for the Efficiency

**Figure 1.**The quantum-mechanical analog of the Carnot cycle depicted in the plane of the volume V and pressure P. During $A\to B$ and $C\to D$, the expectation values of the Hamiltonian are fixed, whereas during $B\to C$ and $D\to A$, the quantum states are kept unchanged.

## 3. Potential Dependence of the Efficiency: Examples

## 4. Conclusion

## Acknowledgment

## References

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Abe, S.
General Formula for the Efficiency of Quantum-Mechanical Analog of the Carnot Engine. *Entropy* **2013**, *15*, 1408-1415.
https://doi.org/10.3390/e15041408

**AMA Style**

Abe S.
General Formula for the Efficiency of Quantum-Mechanical Analog of the Carnot Engine. *Entropy*. 2013; 15(4):1408-1415.
https://doi.org/10.3390/e15041408

**Chicago/Turabian Style**

Abe, Sumiyoshi.
2013. "General Formula for the Efficiency of Quantum-Mechanical Analog of the Carnot Engine" *Entropy* 15, no. 4: 1408-1415.
https://doi.org/10.3390/e15041408