Quantum fluctuation theorem for initial near-equilibrium system

Abstract

Quantum fluctuation theorem (FT) commonly requires the system initially prepared in an equilibrium state. Whether there exists universal exact quantum FT for initial states beyond equilibrium needs further discussions. In the present paper, we initialize the system in a near-equilibrium state, and derive the corresponding modified Jarzynski equality by using perturbation theory. The correction is nontrivial since it directly leads to the principle of maximum work or the second law of thermodynamics for near-equilibrium system, and also offers a much tighter bound of work. Two prototypical near-equilibrium systems driven by a temperature gradient and an external field, are taken into account, to confirm the validity and the generality of our theoretical results. Finally, a fundamental connection between quantum critical phenomenon and near-equilibrium state at really high temperature is revealed.