Transient fluctuation theorem in closed quantum systems

Abstract

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.

5 pages, 6 figures

References in corpus (5)

• Fluctuation theorems: Work is not an observable
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• Typicality for Generalized Microcanonical Ensembles
• Long-Time Behavior of Macroscopic Quantum Systems: Commentary Accompanying the English Translation of John von Neumann's 1929 Article on the Quantum Ergodic Theorem
• Microcanonical quantum fluctuation theorems

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