Quantum Thermodynamics Framework Defines Free Energy and Achieves Reversible Athermality for Channels

Quantum Physics arXiv:2510.12790 (quant-ph) [Submitted on 14 Oct 2025] Title:Thermodynamics of quantum processes: An operational framework for free energy and reversible athermality Authors:Himanshu Badhani, Dhanuja G S, Siddhartha Das View a PDF of the paper titled Thermodynamics of quantum processes: An operational framework for free energy and reversible athermality, by Himanshu Badhani and 2 other authors View PDF HTML (experimental) Abstract:We explore the thermodynamics of quantum processes (quantum channels) by axiomatically introducing the free energy for channels, defined via the quantum relative entropy with an absolutely thermal channel whose fixed output is in equilibrium with a thermal reservoir. This definition finds strong support through its operational interpretations in designated quantum information and thermodynamic tasks. We construct a resource theory of athermality for quantum processes, where free operations are Gibbs preserving superchannels and golden units are unitary channels with respect to absolutely thermal channel having fully degenerate output Hamiltonian. We exactly characterize the one-shot distillation and formation of quantum channels using hypothesis-testing and max-relative entropy with respect to the absolutely thermal channel. These rates converge asymptotically to the channel free energy (up to a multiplicative factor of half the inverse temperature), establishing its operational meaning and proving the asymptotic reversibility of the athermality. We show the direct relation between the resource theory of athermality and quantum information tasks such as private randomness and purity distillation and thermodynamic tasks of erasure and work extraction. Our work connects the core thermodynamic concepts of free energy, energy, entropy, and maximal extractable work of quantum processes to their information processing capabilities. Comments: Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2510.12790 [quant-ph] (or arXiv:2510.12790v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.12790 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Himanshu Badhani [view email] [v1] Tue, 14 Oct 2025 17:58:01 UTC (544 KB) Full-text links: Access Paper: View a PDF of the paper titled Thermodynamics of quantum processes: An operational framework for free energy and reversible athermality, by Himanshu Badhani and 2 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-10 Change to browse by: cond-mat cond-mat.stat-mech hep-th math math-ph math.MP 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?) Links to Code Toggle Papers with Code (What is Papers with Code?) 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?)