Non-equilibrium quantum-heat statistics under stochastic projective measurements

TL;DR

This paper investigates how stochastic timing of quantum measurements influences energy exchange statistics, demonstrating the robustness of quantum fluctuation relations and analyzing heat transfer in two-level systems.

Contribution

It derives a general expression for quantum-heat statistics under stochastic measurements and proves the quantum Jarzynski equality holds in this context.

Findings

Quantum Jarzynski equality remains valid under stochastic measurement protocols.

Analytical characterization of heat transfer in two-level systems.

Effects of stochastic fluctuations and large measurement number analyzed.

Abstract

In this paper we aim at characterizing the effect of stochastic fluctuations on the distribution of the energy exchanged by a quantum system with an external environment under sequences of quantum measurements performed at random times. Both quenched and annealed averages are considered. The information about fluctuations is encoded in the quantum-heat probability density function, or equivalently in its characteristic function, whose general expression for a quantum system with arbitrary Hamiltonian is derived. We prove that, when a stochastic protocol of measurements is applied, the quantum Jarzynski equality is obeyed. Therefore, the fluctuation relation is robust against the presence of randomness in the times intervals between measurements. Then, for the paradigmatic case of a two-level system, we analytically characterize the quantum-heat transfer. Particular attention is devoted to the limit of large number of measurements and to the effects caused by the stochastic fluctuations. The relation with the stochastic Zeno regime is also discussed.