Work statistics via real-time effective field theory: Application to work extraction from a thermal bath with qubit coupling

Quantum thermal states are known to be passive, as required by the second law of thermodynamics. This paper investigates the potential for work extraction by coupling a thermal bath to a qubit of either spin, fermionic, or topological type, which acts as a quantum thermal state at different temperatures. The amount of work extraction is derived from the work statistics under a cyclic nonequilibrium process. Although the work statistics of many-body systems are known to be challenging to calculate explicitly, we propose an effective field theory approach to tackle this problem by assuming the externally driven source couples to a specific quasiparticle operator of the thermal state. We show that the work statistics can be expressed succinctly in terms of this quasiparticle's thermal spectral function. We obtain the nonperturbative work distribution function (WDF) for the pure thermal bath without the qubit coupling. With qubit coupling, we get the second-order WDF, from which the physical regime of work extraction can be pinned down precisely to help devise quantum heat engines or refrigerators. Their efficiency or coefficient of performance can be inferred from the combination of the fluctuation theorem and the first law, and we find that the spin or topological qubit-bath system generally yields a far better heat engine or refrigerator than the other two alternatives due to the underlying quantum statistics.