Transient fluctuation theorem in closed quantum systems
Fachbereich Physik, Universität Osnabrück - Barbarastrasse 7, D-49069 Osnabrück, Germany, EU
Accepted: 2 November 2011
Our point of departure are the unitary dynamics of closed quantum systems as generated from the Schrödinger equation. We focus on a class of quantum models that typically exhibit roughly exponential relaxation of some observable within this framework. Furthermore, we focus on pure state evolutions. An entropy in accord with Jaynes principle is defined on the basis of the quantum expectation value of the above observable. It is demonstrated that the resulting deterministic entropy dynamics are in a sense in accord with a transient fluctuation theorem. Moreover, we demonstrate that the dynamics of the expectation value are describable in terms of an Ornstein-Uhlenbeck process. These findings are demonstrated numerically and supported by analytical considerations based on quantum typicality.
PACS: 05.30.-d – Quantum statistical mechanics / 03.65.Yz – Decoherence; open systems; quantum statistical methods / 05.70.Ln – Nonequilibrium and irreversible thermodynamics
© EPLA, 2011