Geometric quantum thermodynamics: A fibre bundle approach

• URL: http://arxiv.org/abs/2512.14383v2
• Date: Tue, 23 Dec 2025 16:37:54 GMT
• Title: Geometric quantum thermodynamics: A fibre bundle approach
• Authors: T. Pernambuco, L. C. Céleri,
• Abstract summary: In quantum mechanics, information theory plays an important role in describing the thermal properties of quantum systems.<n>Recently, a new approach has been proposed in the form of a quantum thermodynamic gauge theory.<n>We show that there are two distinct geometric structures associated with the gauge theory of quantum thermodynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Classical thermodynamics is a theory based on coarse-graining, meaning that the thermodynamic variables arise from discarding information related to the microscopic features of the system at hand. In quantum mechanics, however, where one has a high degree of control over microscopic systems, information theory plays an important role in describing the thermal properties of quantum systems. Recently, a new approach has been proposed in the form of a quantum thermodynamic gauge theory, where the notion of redundant information arises from a group of physically motivated gauge transformations called the thermodynamic group. In this work, we explore the geometrical structure of quantum thermodynamics. Particularly, we do so by explicitly constructing the relevant principal fibre bundle. We then show that there are two distinct (albeit related) geometric structures associated with the gauge theory of quantum thermodynamics. In this way, we express thermodynamics in the same mathematical (geometric) language as the fundamental theories of physics. Finally, we discuss how the geometric and topological properties of these structures may help explain fundamental properties of thermodynamics.

Related papers

• Algorithmic Quantum Simulations of Quantum Thermodynamics [22.18998680528792]
  We develop protocols for simulating quantum thermodynamics on quantum hardware through quantum kernel function expansion (QKFE)<n>These protocols are demonstrated by simulating transverse field Ising and XY models with superconducting qubits.<n>Our approach provides a general framework for computing thermodynamic potentials on programmable quantum devices.
  arXiv  Detail & Related papers  (2025-11-28T06:06:23Z)
• The Large-Scale Structure of Entanglement in Quantum Many-body Systems [44.99833362998488]
  We show that the thermodynamic limit of a many-body system can reveal entanglement properties that are hard to detect in finite-size systems.<n>In particular, we show that every gapped phase of matter, even the trivial one, in $Dgeq 2$ dimensions contains models with the strongest possible bipartite large-scale entanglement.
  arXiv  Detail & Related papers  (2025-03-05T19:01:05Z)
• Quantum thermodynamics as a gauge theory [0.0]
  A gauge theory for quantum thermodynamics was introduced, defining gauge invariant work and heat.<n>We extend that theory in two significant ways, incorporating energy spectrum degeneracies, which were previously overlooked.<n>This results in a complete framework for quantum thermodynamics grounded in the principle of gauge invariance.
  arXiv  Detail & Related papers  (2024-09-12T00:46:48Z)
• Thermodynamics-Consistent Graph Neural Networks [50.0791489606211]
  We propose excess Gibbs free energy graph neural networks (GE-GNNs) for predicting composition-dependent activity coefficients of binary mixtures. The GE-GNN architecture ensures thermodynamic consistency by predicting the molar excess Gibbs free energy. We demonstrate high accuracy and thermodynamic consistency of the activity coefficient predictions.
  arXiv  Detail & Related papers  (2024-07-08T06:58:56Z)
• Quantum thermodynamics of nonequilibrium processes in lattice gauge theories [0.0]
  We show how to define thermodynamic quantities using strong-coupling thermodynamics.<n>Our definitions suit instantaneous quenches, simple nonequilibrium processes undertaken in quantum simulators.
  arXiv  Detail & Related papers  (2024-04-03T18:00:03Z)
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics [62.997667081978825]
  In quantum mechanics, the energy per degree of freedom is not equally distributed. We show that in the high-temperature regime, the classical result is recovered.
  arXiv  Detail & Related papers  (2022-05-24T20:51:03Z)
• Gauge Quantum Thermodynamics of Time-local non-Markovian Evolutions [77.34726150561087]
  We deal with a generic time-local non-Markovian master equation. We define current and power to be process-dependent as in classical thermodynamics. Applying the theory to quantum thermal engines, we show that gauge transformations can change the machine efficiency.
  arXiv  Detail & Related papers  (2022-04-06T17:59:15Z)
• Gauge invariant quantum thermodynamics: consequences for the first law [0.0]
  Information theory plays a major role in the identification of thermodynamic functions. We explicitly construct physically motivated gauge transformations which encode a gentle variant of coarse-graining behind thermodynamics. As a consequence, we reinterpret quantum work and heat, as well as the role of quantum coherence.
  arXiv  Detail & Related papers  (2021-04-20T17:53:16Z)
• Geometric Quantum Thermodynamics [0.0]
  Building on parallels between geometric quantum mechanics and classical mechanics, we explore an alternative basis for quantum thermodynamics. We develop both microcanonical and canonical ensembles, introducing continuous mixed states as distributions on the manifold of quantum states. We give both the First and Second Laws of Thermodynamics and Jarzynki's Fluctuation Theorem.
  arXiv  Detail & Related papers  (2020-08-19T21:55:25Z)
• Entropy, Divergence, and Majorization in Classical and Quantum Thermodynamics [0.0]
  It has been revealed that there is rich information-theoretic structure in thermodynamics of out-of-equilibrium systems in both the classical and quantum regimes. Main purpose of this book is to clarify how information theory works behind thermodynamics and to shed modern light on it.
  arXiv  Detail & Related papers  (2020-07-20T09:50:27Z)
• Temperature of a finite-dimensional quantum system [68.8204255655161]
  A general expression for the temperature of a finite-dimensional quantum system is deduced from thermodynamic arguments. Explicit formulas for the temperature of two and three-dimensional quantum systems are presented.
  arXiv  Detail & Related papers  (2020-05-01T07:47:50Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.