A note on the Landauer principle in quantum statistical mechanics

Abstract

The Landauer principle asserts that the energy cost of erasure of one bit of information by the action of a thermal reservoir in equilibrium at temperature T is never less than kBT log 2. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system \documentclass[12pt]{minimal}\begin{document}${\cal S}$\end{document}S coupled to an infinitely extended thermal reservoir \documentclass[12pt]{minimal}\begin{document}${\cal R}$\end{document}R. Using Araki's perturbation theory of KMS states and the Avron-Elgart adiabatic theorem we prove, under a natural ergodicity assumption on the joint system \documentclass[12pt]{minimal}\begin{document}${\cal S}+{\cal R}$\end{document}S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work [Reeb, D. and Wolf M. M., “(Im-)proving Landauer's principle,” preprint arXiv:1306.4352v2 (2013)] on the subject is discussed and compared.