A note on the Landauer principle in quantum statistical mechanics

Vojkan Jaksic (1) , Claude-Alain Pillet (2, 3, 4)

1 Department of Mathematics and Statistics [Montréal]
2 FRUMAM - Fédération de Recherche des Unités de MAthématiques de Marseille
3 CPT - E5 Physique statistique et systèmes complexes
4 CPT - Centre de Physique Théorique - UMR 7332

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 kT log 2. We discuss Landauer's principle for quantum statistical models describing a finite level quantum system S coupled to an infinitely extended thermal reservoir 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 S+R, that Landauer's bound saturates for adiabatically switched interactions. The recent work of Reeb and Wolf on the subject is discussed and compared.

Mots clés: nonequilibrium statistical mechanics; thermodynamics of computation

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Mécanique statistique [cond-mat.stat-mech]

Vojkan Jaksic, Claude-Alain Pillet. A note on the Landauer principle in quantum statistical mechanics. Journal of Mathematical Physics, 2014, 55, pp.075210. ⟨10.1063/1.4884475⟩. ⟨hal-00998251⟩