Quantum fluctuation theorem for initial near-equilibrium system

TL;DR

This paper derives a modified quantum work fluctuation theorem for near-equilibrium states, extending the traditional equilibrium-based theorem and revealing connections to thermodynamics and quantum critical phenomena.

Contribution

It introduces a perturbation-based derivation of a quantum fluctuation theorem applicable to near-equilibrium states, expanding the scope beyond equilibrium initial conditions.

Findings

Derived a modified Jarzynski equality for near-equilibrium states

Established a connection between quantum critical phenomena and near-equilibrium thermodynamics

Verified theoretical results with a many-body system at high temperature

Abstract

Quantum work fluctuation theorem (FT) commonly requires the system initially prepared in an equilibrium state. Whether there exists universal exact quantum work FT for initial state beyond equilibrium needs further discussions. Here, I initialize the system in a near-equilibrium state, and derive the corresponding modified Jarzynski equality by using the perturbation theory. The correction is nontrivial because it directly leads to the principle of maximum work or the second law of thermodynamics for near-equilibrium system and also gives a much tighter bound of work for a given process. I also verify my theoretical results by considering a concrete many-body system, and reveal a fundamental connection between quantum critical phenomenon and near-equilibrium state at really high temperature.