Autonomization of Quantum Systems and the Emergence of the Work Operator

Quantum Physics arXiv:2607.20602 (quant-ph) [Submitted on 22 Jul 2026] Title:Autonomization of Quantum Systems and the Emergence of the Work Operator Authors:Carlo Cepollaro, Danial Chughtai, Alberto Spalvieri, Marcus Huber, Alberto Rolandi View a PDF of the paper titled Autonomization of Quantum Systems and the Emergence of the Work Operator, by Carlo Cepollaro and 4 other authors View PDF Abstract:Estimation of work at the quantum scale remains a central challenge in quantum thermodynamics. Canonical approaches have a fundamental drawback: they assume classical control of the quantum system, as implicit in a time-dependent Hamiltonian. Yet the energetic cost of implementing this control is omitted and can exceed the system's energy scale by orders of magnitude, calling into question the operational significance of work values. We address this by autonomizing the controlled energy transfer, embedding the driven dynamics into an energy-conserving evolution on a larger quantum system. Work is then unambiguously identified with the energy transferred between the two systems, singling out a unique observable on the driven system: the work operator. We show that the quantum work operator evades a no-go theorem by deriving a quantum fluctuation theorem that recovers the Jarzynski equality in classical scenarios. We incorporate imperfect control and quantify corrections to work statistics. Extending the framework to open quantum systems, we obtain an operatorial first law in which work, heat, and internal-energy changes are represented by distinct operators on the reduced system. Together, these results settle the long-standing debate over whether work is a quantum observable: it is, once the controlling system is included in the description rather than treated as external. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2607.20602 [quant-ph] (or arXiv:2607.20602v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2607.20602 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Carlo Cepollaro [view email] [v1] Wed, 22 Jul 2026 18:00:00 UTC (1,021 KB) Full-text links: Access Paper: View a PDF of the paper titled Autonomization of Quantum Systems and the Emergence of the Work Operator, by Carlo Cepollaro and 4 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-07 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)