Similarity between quantum mechanics and thermodynamics: Entropy, temperature, and Carnot cycle

TL;DR

This paper explores the formal similarities between quantum mechanics and thermodynamics, demonstrating how Shannon entropy aligns with von Neumann entropy and analyzing a quantum Carnot cycle with classical efficiency.

Contribution

It establishes a formal connection between Shannon and von Neumann entropies under Clausius equality and studies a quantum Carnot cycle with classical efficiency.

Findings

Shannon entropy coincides with von Neumann entropy under certain conditions.

Quantum Carnot cycle efficiency matches classical Carnot efficiency.

Pure-state quantum mechanics can be viewed as quantum thermodynamics.

Abstract

Similarity between quantum mechanics and thermodynamics is discussed. It is found that if the Clausius equality is imposed on the Shannon entropy and the analogue of the heat quantity, 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.