Energy fluctuation relations and repeated quantum measurements

Year: 2022

Authors: Gherardini S.; Buffoni L.; Giachetti G.; Trombettoni A.; Ruffo S.

Autors Affiliation: CNR-INO, Area Science Park, Basovizza, Trieste, I-34149, Italy; SISSA, via Bonomea 265, Trieste, & INFN, I-34136, Italy; LENS, University of Florence, via G. Sansone 1, Sesto Fiorentino, I-50019, Italy; Physics of Information and Quantum Technologies Group, Instituto de Telecomunicazkhes, University of Lisbon, Av. Rovisco Pais, Lisbon, P-1049-001, Portugal; SISSA and INFN, Sezione di Trieste, Via Bonomea 265, Trieste, & INFN, I-34136, Italy; Department of Physics, University of Trieste, Strada Costiera 11, Trieste, I-34151, Italy; CNR-IOM DEMOCRITOS Simulation Center, Via Bonomea 265, Trieste, I-34136, Italy; Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche, via Madonna del Piano 10, Sesto Fiorentino, I-50019, Italy

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-?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


Volume: 156      Pages from: 111890-1  to: 111890-10

More Information: Discussions with A. Belenchia, M. Campisi, P. Cappellaro, F.S. Cataliotti, D. Cohen, N. Fabbri, S. Hernandez-Gomez, M. Paternostro, F. Poggiali and A. Sone are gratefully acknowledged. The authors acknowledge the MISTI Global Seed Funds MIT-FVG collaboration grants “NV centers for the test of the Quantum Jarzynski Equality (NVQJE)” and “Non-Equilibrium Thermodynamics of Dissipative Quantum Systems”, and the MIUR-PRIN2017 project “Coarsegrained description for non-equilibrium systems and transport phenomena (CO-NEST)” No. 201798CZL. S.G. also acknowledges The Blanceflor Foundation for financial support through the project “The theRmodynamics behInd thE meaSuremenT postulate of quantum mEchanics (TRIESTE)” awarded in 2021. Support form the Progetto Bilaterale CNR/RS “Testing fundamental theories with ultracold atoms” is also acknowledged.
KeyWords: Fluctuations relations; Quantum measurements; Quantum thermodynamics
DOI: 10.1016/j.chaos.2022.111890