Nonequilibrium work equalities in isolated quantum systems

Vyacheslav I. Yukalov

Fei Liu, Zhong-Can Ouyang

We briefly introduce the quantum Jarzynski and Bochkov-Kuzovlev equalities in isolated quantum Hamiltonian systems, which includes the origin of the equalities, their derivations using a quantum Feynman-Kac formula, the quantum Crooks equality, the evolution equations governing the characteristic functions of the probability density functions for the quantum work, the recent experimental verifications. Some results are given here first time. We particularly emphasize the formally structural consistence between these quantum equalities and their classical counterparts, which shall be useful in understanding the existing equalities and pursuing new fluctuation relations in other complex quantum systems.

Fei Liu

On the basis of a quantum mechanical analog of the famous Feynman-Kac formula, we present a method to derive nonequilibrium work equalities for isolated quantum systems, which include the Jarzynski equality and Bochkov-Kuzovlev equality. Compared with other methods in the literature, our method shows a higher similarity in form to the method deriving the fluctuation relations in the classical systems.

V. V. Mityugov

Tim Langen

Zongping Gong, Yuto Ashida, Masahito Ueda

We employ the quantum-jump-trajectory approach to construct a systematic framework to study the thermodynamics at the trajectory level in a nonequilibrium open quantum system under discrete feedback control. Within this framework, we derive quantum versions of the generalized Jarzynski equalities, which are demonstrated in an isolated pseudospin system and a coherently driven two-level open quantum system. Due to quantum coherence and measurement backaction, a fundamental distinction from the classical generalized Jarzynski equalities emerges in the quantum versions, which is characterized by a large negative information gain reflecting genuinely quantum rare events. A possible experimental scheme to test our findings in superconducting qubits is discussed.