Energy fluctuation relations and repeated quantum measurements

Abstract

In this review paper, we discuss the statistical description in non-equilibrium regimes of energy fluctuations originated by the interaction between a quantum system and a measurement apparatus applying a sequence of repeated quantum measurements. To properly quantify the information about energy fluctuations, both the exchanged heat probability density function and the corresponding characteristic function are derived and interpreted. Then, we discuss the conditions allowing for the validity of the fluctuation theorem in Jarzynski form $⟨e^{-\beta Q}⟩=1$, thus showing that the fluctuation relation is robust against the presence of randomness in the time intervals between measurements. Moreover, also the late-time, asymptotic properties of the heat characteristic function are analyzed, in the thermodynamic limit of many intermediate quantum measurements. In such a limit, the quantum system tends to the maximally mixed state (thus corresponding to a thermal state with infinite temperature) unless the system's Hamiltonian and the intermediate measurement observable share a common invariant subspace. Then, in this context, we also discuss how energy fluctuation relations change when the system operates in the quantum Zeno regime. Finally, the theoretical results are illustrated for the special cases of two- and three-levels quantum systems, now ubiquitous for quantum applications and technologies.

15 pages, 1 figure. Contribution to the Special Issue "In Memory of Tito Arecchi" in the journal "Chaos, Solitons & Fractals"

References in corpus (11)

• Fluctuation theorems: Work is not an observable
• Second Law of Thermodynamics with Discrete Quantum Feedback Control
• Quantum Zeno dynamics: mathematical and physical aspects
• Fluctuation Theorem for Arbitrary Open Quantum Systems
• The role of quantum measurement in stochastic thermodynamics
• Nonequilibrium fluctuations in quantum heat engines: Theory, example, and possible solid state experiments
• Stabilizing Open Quantum Batteries by Sequential Measurements
• Fluctuation theorems for continuously monitored quantum fluxes
• Holevo's bound from a general quantum fluctuation theorem
• Influence of measurements on the statistics of work performed on a quantum system
• Experimental verification of fluctuation relations with a quantum computer