Role of the superposition principle for enhancing the efficiency of the quantum-mechanical Carnot engine.

The role of the superposition principle is discussed for the quantum-mechanical Carnot engine introduced by Bender, Brody, and Meister [J. Phys. A 33, 4427 (2000)]. It is shown that the efficiency of the engine can be enhanced by the superposition of quantum states. A finite-time process is also discussed and the condition of the maximum power output is presented. Interestingly, the efficiency at the maximum power is lower than that without superposition.

Similarity between quantum mechanics and thermodynamics: entropy, temperature, and Carnot cycle.

The similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analog of the quantity of heat, then the value of the Shannon entropy comes to formally coincide with that of the von Neumann entropy of the canonical density matrix, and pure-state quantum mechanics apparently transmutes into quantum thermodynamics. The corresponding quantum Carnot cycle of a simple two-state model of a particle confined in a one-dimensional infinite potential well is studied, and its efficiency is shown to be identical to the classical one.