Geometric Thermodynamics in Open Quantum Systems: Coherence, Curvature, and Work

Quantum Physics [Submitted on 23 Mar 2026] Geometric Thermodynamics in Open Quantum Systems: Coherence, Curvature, and Work Eric R. Bittner We formulate a geometric framework for quasistatic thermodynamics in open quantum systems by parameterizing the dynamics on a control manifold. In the quasistatic limit, the system follows a manifold of stationary states, and the work performed over a cycle is given by the flux of a curvature two-form, W \sim \int \Omega, defined by the parametric response of the stationary state, establishing an open-system analog of classical thermodynamic area laws. For thermal stationary states, the curvature is isotropic and depends only on the instantaneous energy scale, yielding a population-driven geometry in which environmental parameters reshape how work is distributed across the control manifold. Beyond this limit, nonequilibrium stationary states can retain coherence in the energy representation; using a fixed-basis Lindblad model, we show that this coherence reshapes the curvature, making it anisotropic and sign-changing, so that work depends sensitively on the placement and orientation of the cycle. Quantum coherence therefore partitions the control manifold into regions of opposite curvature, producing geometric cancellation of work and allowing the net work over a cycle to be reduced or reversed despite dissipative dynamics. Thermodynamic work thus emerges as a curvature flux whose structure is set by thermodynamic response in classical systems and by basis misalignment between the Hamiltonian eigenbasis and the environment-selected pointer basis in open quantum systems. Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech) Cite as: arXiv:2603.22452 [quant-ph]   (or arXiv:2603.22452v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.22452 Focus to learn more Submission history From: Eric R. Bittner [view email] [v1] Mon, 23 Mar 2026 18:21:19 UTC (528 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cond-mat cond-mat.stat-mech References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)