Energy fluctuation relations and repeated quantum measurements. (March 2022)

• Record Type: Journal Article
• Authors: Gherardini, Stefano; Buffoni, Lorenzo; Giachetti, Guido; Trombettoni, Andrea; Ruffo, Stefano
• Is Part Of: Chaos, solitons and fractals. Volume 156(2022)
• Publication Date: 2022-03
• Subjects: Quantum measurements -- Quantum thermodynamics -- Fluctuations relations; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2022.111890
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: Derivation of the characteristic function for a process of repeated quantum measurements. Discussion on the validity of the Jarzynski fluctuation theorem, showing that is robust against randomness in the time intervals between measurements. Discussion of some singular limits of the characteristic function, namely the thermodynamics limit of many intermediate measures and the quantum Zeno limit. Explicit derivations for 2 and 3 level quantum systems. Abstract: In this 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 − β 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.