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arxiv: 2512.14383 · v3 · submitted 2025-12-16 · 🪐 quant-ph

Geometric quantum thermodynamics: A fibre bundle approach

T. Pernambuco , L. C. C\'eleri This is my paper

Pith reviewed 2026-05-16 21:50 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum thermodynamicsfibre bundlegauge theoryprincipal bundlethermodynamic groupgeometric structurequantum information
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The pith

Quantum thermodynamics is recast as a principal fibre bundle with the thermodynamic group as structure group.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The authors explicitly construct the principal fibre bundle whose fibres are the orbits of the thermodynamic group, the set of gauge transformations that remove redundant microscopic information from a quantum state. They then identify two distinct but related geometric structures on this bundle that together encode the gauge theory of quantum thermodynamics. This construction places thermodynamic variables and relations in the same geometric language used for fundamental interactions. A reader would care because the geometric and topological features of the bundle are proposed to underlie basic thermodynamic properties such as equilibrium and irreversibility.

Core claim

By building the principal fibre bundle associated with the thermodynamic group, the work shows that quantum thermodynamics admits two related geometric structures. These structures allow the entire theory to be written in the same mathematical language as gauge theories, thereby opening the possibility that geometric and topological properties of the bundle explain the fundamental features of thermodynamics.

What carries the argument

The principal fibre bundle whose base space is the manifold of thermodynamic states and whose structure group is the thermodynamic group of gauge transformations that discard redundant information.

If this is right

  • Thermodynamic relations acquire a geometric interpretation identical to that of gauge fields.
  • Topological invariants of the bundle become candidates for conserved or quantized thermodynamic quantities.
  • Equilibrium states correspond to horizontal sections or flat connections on the bundle.
  • The two geometric structures imply that classical and quantum thermodynamic descriptions are related by a change of bundle trivialization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same bundle construction might be used to geometrize fluctuation theorems or thermodynamic uncertainty relations.
  • Singularities or non-trivial topology in the bundle could correspond to phase transitions or critical points.
  • Connection forms on the bundle may supply a natural definition of thermodynamic work and heat in open quantum systems.

Load-bearing premise

The thermodynamic group supplies a complete and physically correct collection of gauge transformations that capture every piece of redundant microscopic information without requiring extra dynamical assumptions.

What would settle it

An explicit computation for a two-level system or harmonic oscillator showing that the curvature or connection of the constructed bundle fails to reproduce the first law or the entropy functional of standard quantum thermodynamics.

Figures

Figures reproduced from arXiv: 2512.14383 by L. C. C\'eleri, T. Pernambuco.

Figure 1
Figure 1. Figure 1: The coarse graining process defined by restrict [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The action of the thermodynamic group GT . The orbits (orange blobs), created by the group action g · ρ (which is just conjugation by the matrices Vt) are subspaces of density matrices that are indistinguishable for the measurement scheme that defines the group. where × denotes the Cartesian product and U(n i t ) is the unitary group of dimension n i t , the (in general, time-dependent) degeneracy of the i… view at source ↗
Figure 3
Figure 3. Figure 3: A simple example of a bundle. The base space [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims to explicitly construct the principal fibre bundle associated with the thermodynamic group of gauge transformations in quantum thermodynamics, identify two distinct but related geometric structures arising from this gauge theory, and use the resulting geometric and topological properties to express thermodynamics in the same mathematical language as fundamental gauge theories.

Significance. If the central construction is made rigorous, the work would supply a differential-geometric realization of quantum thermodynamics that parallels the fibre-bundle formulation of gauge theories, potentially allowing topological invariants to constrain thermodynamic relations and offering a unified language for coarse-graining and information redundancy.

major comments (2)
  1. [Abstract; main construction (presumably §3–4)] The abstract and introduction assert an explicit construction of the principal fibre bundle, yet no definition of the total space, base manifold, projection map, or transition functions is supplied, nor is the thermodynamic group action shown to be free and proper on the space of density operators (required for the quotient to be a smooth manifold and the structure to be a principal G-bundle).
  2. [Section on geometric structures] The existence of two distinct geometric structures is stated without explicit derivations, local trivializations, or concrete examples demonstrating how each structure is induced from the bundle; this leaves the central claim that thermodynamics is thereby expressed in the language of gauge theory without load-bearing support.
minor comments (2)
  1. [Introduction] Clarify the precise definition of the thermodynamic group and its action on quantum states at the outset, including any assumptions on the underlying Hilbert space or density-operator manifold.
  2. [Discussion] Add a brief comparison with existing geometric approaches to quantum thermodynamics (e.g., information-geometric or symplectic formulations) to situate the fibre-bundle construction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. The comments correctly identify that the principal-bundle construction and the two geometric structures require more explicit definitions, derivations, and supporting details to meet the standards of a rigorous gauge-theoretic formulation. We will revise the manuscript to address both points fully.

read point-by-point responses

  1. Referee: [Abstract; main construction (presumably §3–4)] The abstract and introduction assert an explicit construction of the principal fibre bundle, yet no definition of the total space, base manifold, projection map, or transition functions is supplied, nor is the thermodynamic group action shown to be free and proper on the space of density operators (required for the quotient to be a smooth manifold and the structure to be a principal G-bundle).

    Authors: We agree that the current text does not supply the required definitions or the verification that the thermodynamic group action is free and proper. In the revised manuscript we will (i) explicitly define the total space as the appropriate space of density operators equipped with the thermodynamic group action, (ii) identify the base manifold as the space of thermodynamic equivalence classes, (iii) give the projection map, (iv) construct local trivializations and transition functions, and (v) prove that the action is free and proper so that the quotient is a smooth manifold and the structure is a principal G-bundle. revision: yes

  2. Referee: [Section on geometric structures] The existence of two distinct geometric structures is stated without explicit derivations, local trivializations, or concrete examples demonstrating how each structure is induced from the bundle; this leaves the central claim that thermodynamics is thereby expressed in the language of gauge theory without load-bearing support.

    Authors: We accept that the two geometric structures are asserted rather than derived in detail. The revised version will contain (i) explicit derivations showing how each structure arises from the principal bundle, (ii) the corresponding local trivializations, and (iii) at least one concrete low-dimensional example (e.g., a two-level system) that illustrates the induction of both structures and their relation to thermodynamic quantities. revision: yes

Circularity Check

0 steps flagged

No significant circularity: fibre-bundle construction is an independent geometric application

full rationale

The paper starts from the recently proposed thermodynamic gauge group (treated as an external input) and applies standard principal-bundle constructions from differential geometry. No derivation step reduces by construction to its own fitted parameters, self-defined quantities, or a load-bearing self-citation chain. The claim that the group action yields a principal bundle rests on the physical-motivation assumption rather than on any equation that tautologically reproduces its input. The two geometric structures are presented as realizations of that input, not as predictions forced by the input itself. This is the normal, non-circular case of importing a premise and then performing independent mathematical work on it.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption of the thermodynamic group and the standard axioms of principal fibre bundles; no free parameters or new invented entities are introduced in the abstract.

axioms (1)
  • domain assumption The thermodynamic group is a well-defined collection of physically motivated gauge transformations that encode redundant information in quantum thermodynamic descriptions.
    Invoked as the foundation of the gauge theory whose bundle is constructed.

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Geometry of restricted information: the case of quantum thermodynamics

    quant-ph 2026-02 unverdicted novelty 7.0

    A gauge-invariant formulation of quantum thermodynamics is constructed from restricted information, yielding a stochastic invariant entropy that obeys detailed fluctuation theorems and unifies the first and second law...

Reference graph

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