Quantum work fluctuation theorem: Nonergodic Brownian motion case

R. L. Hudson, J. Martin Lindsay

Hing-Tong Cho, B. L. Hu

Zhan-Wu Bai

For a system in which free quantum Brownian particles interact with a non-Markovian heat bath with product initial states, the quantum heat-fluctuation theorems and the Jarzynski relation of the reduced system are derived using the path integral technique. They are not a direct generalization of the classical case. The validity of the second law of quantum thermodynamics is shown. The forms of these theorems and relations have to do with the specified nonequilibrium initial states, and are dependent on the structure of the bath (ergodic or nonergodic) in the quantum case as well as the classical case under some initial states.

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

Ilki Kim, Günter Mahler A

G. W. Ford, Robert F. O’Connell

The Onsager regression hypothesis states that the regression of fluctuations is governed by macroscopic equations describing the approach to equilibrium. It is here asserted that this hypothesis fails in the quantum case. This is shown first by explicit calculation for the example of quantum Brownian motion of an oscillator and then in general from the fluctuation-dissipation theorem. It is asserted that the correct generalization of the Onsager hypothesis is the fluctuation-dissipation theorem.