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arxiv: 2602.06716 · v2 · pith:JCIF7FMMnew · submitted 2026-02-06 · 🪐 quant-ph

Geometry of restricted information: the case of quantum thermodynamics

Tiago Pernambuco , Lucas Chibebe C\'eleri This is my paper

Pith reviewed 2026-05-21 14:16 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum thermodynamicsgauge symmetryfluctuation theoremrestricted informationgeometric frameworkentropy productioninvariant entropyClausius inequality
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The pith

Modeling measurement constraints as gauge symmetries on quantum states yields gauge-invariant thermodynamics with a detailed fluctuation theorem and unified laws.

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

The paper develops a geometric approach in which physical laws arise because observers have only restricted access to full microscopic information. Measurement limits are represented by treating them as gauge symmetries acting on density operators, which creates a reduced space containing only physically distinguishable states. Applied to quantum thermodynamics, the construction produces an invariant entropy that follows a stochastic description and obeys a general detailed fluctuation theorem. This permits derivation of an integrated fluctuation theorem together with a Clausius-like inequality that combines the first and second laws through invariant work and coherent heat. Irreversibility is expressed as relative entropy between forward and backward trajectory probabilities on the reduced space, while the third law appears as the collapse of orbits at zero temperature.

Core claim

We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of physically distinguishable states. In the case of quantum thermodynamics, this construction leads to a gauge-invariant formulation in which the invariant entropy admits a stochastic description and satisfies a general detailed fluctuation theorem. From this result, we derive an integrated fluctuation theorem and a Clausius-like inequality that unifies the first and second laws in terms of invariant work and coherent heat. Entropy production is identified with a

What carries the argument

Gauge symmetry acting on density operators, inducing a gauge-reduced space of physically distinguishable states. The symmetry restricts observable information so that invariant quantities satisfy thermodynamic fluctuation relations and inequalities.

If this is right

  • The invariant entropy admits a stochastic description and satisfies a general detailed fluctuation theorem.
  • An integrated fluctuation theorem and Clausius-like inequality unify the first and second laws in terms of invariant work and coherent heat.
  • Entropy production equals the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories.
  • The third law emerges as a singular zero-temperature limit in which thermodynamic orbits collapse and entropy production vanishes.
  • Standard energy-based thermodynamics is recovered as one particular case among arbitrary information constraints.

Where Pith is reading between the lines

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

  • The same gauge-reduction construction could be tested in quantum information protocols where only partial measurements are available.
  • One could examine whether the coherent-heat term matches calorimetric data in engineered quantum heat engines with tunable observation limits.
  • The geometric collapse of orbits at zero temperature offers a way to reinterpret unattainability of absolute zero in other constrained systems.

Load-bearing premise

Measurement constraints can be modeled as a gauge symmetry acting on density operators that induces a gauge-reduced space of physically distinguishable states.

What would settle it

A controlled quantum thermodynamic experiment that imposes partial observation restrictions and checks whether the resulting invariant entropy obeys the predicted detailed fluctuation theorem; systematic violation would falsify the construction.

Figures

Figures reproduced from arXiv: 2602.06716 by Lucas Chibebe C\'eleri, Tiago Pernambuco.

Figure 2
Figure 2. Figure 2: The thermodynamic work Wu = Winv − Qc is plotted against the bound of eq. (D3). At the phase tran￾sition, an energy cost T SΓ associated to the generation of degeneracies arises. Due to the dynamics depending only on the z-magnetization, the system presents no co￾herence. It is very interesting to note that, since the degeneracy appears suddenly at t = 5, the bound in (B12) states that the work performed o… view at source ↗
read the original abstract

We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of physically distinguishable states. In the case of quantum thermodynamics, this construction leads to a gauge-invariant formulation in which the invariant entropy admits a stochastic description and satisfies a general detailed fluctuation theorem. From this result, we derive an integrated fluctuation theorem and a Clausius-like inequality that unifies the first and second laws in terms of invariant work and coherent heat. Entropy production is identified with the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories, revealing irreversibility as a geometric consequence of limited observability. The third law emerges as a singular zero-temperature limit in which thermodynamic orbits collapse and entropy production vanishes. Since the framework applies to arbitrary information constraints, it encompasses energy-based thermodynamics as a particular case of more general measurement scenarios.

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

1 major / 1 minor

Summary. The manuscript develops a geometric framework in which measurement constraints are modeled as gauge symmetries acting on density operators, inducing a gauge-reduced space of physically distinguishable states. In quantum thermodynamics this yields a gauge-invariant formulation in which an invariant entropy admits a stochastic description and obeys a general detailed fluctuation theorem. From this the authors derive an integrated fluctuation theorem and a Clausius-like inequality that unifies the first and second laws in terms of invariant work and coherent heat. Entropy production is identified with the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories, and the third law appears as a singular zero-temperature limit in which orbits collapse and production vanishes. The construction is presented as encompassing energy-based thermodynamics as a special case of arbitrary information constraints.

Significance. If the gauge invariance of the measures and the subsequent derivations can be rigorously established, the work supplies a geometric interpretation of irreversibility as a consequence of restricted observability and offers a unified treatment of fluctuation theorems together with a Clausius-like relation. The emergence of the third law as a geometric limit and the claimed generality to non-energy constraints are potentially valuable, though the manuscript must demonstrate that these results are not artifacts of representative choice.

major comments (1)
  1. [Framework description and derivation of the detailed fluctuation theorem] Framework description and derivation of the detailed fluctuation theorem: the forward and backward probability measures on the gauge-reduced space of trajectories must be shown to be canonically defined on the quotient without reference to a particular lift or section. The manuscript does not specify the projection or averaging procedure that would render the relative entropy (and hence the fluctuation theorems and Clausius-like inequality) independent of representative choice; if an implicit gauge fixing is used, the claimed invariance is undermined.
minor comments (1)
  1. [Abstract] The abstract packs multiple technical claims into single sentences; splitting the description of the stochastic representation, the detailed theorem, and the unified inequality would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for identifying the need to clarify the canonical construction of the probability measures on the gauge-reduced space. We address this point below and will incorporate the requested details in a revised version.

read point-by-point responses

  1. Referee: Framework description and derivation of the detailed fluctuation theorem: the forward and backward probability measures on the gauge-reduced space of trajectories must be shown to be canonically defined on the quotient without reference to a particular lift or section. The manuscript does not specify the projection or averaging procedure that would render the relative entropy (and hence the fluctuation theorems and Clausius-like inequality) independent of representative choice; if an implicit gauge fixing is used, the claimed invariance is undermined.

    Authors: We agree that an explicit demonstration of canonical definition on the quotient is essential. In our geometric construction the gauge-reduced space is the quotient manifold obtained by the free and proper action of the gauge group on the space of density operators. The forward and backward probability measures on the space of thermodynamic trajectories are defined intrinsically on this quotient by pushing forward the stochastic process via the natural projection map and averaging with respect to the invariant Haar measure on the gauge group. This averaging renders both measures independent of any choice of section or lift, so that the relative entropy between them is a gauge-invariant functional on the reduced trajectory space. We acknowledge that the original manuscript did not spell out this projection-and-averaging step in sufficient detail. In the revised version we will add a dedicated subsection that (i) defines the projection map from the unreduced trajectory space to the gauge-reduced space, (ii) states the averaging procedure using the Haar measure, and (iii) proves that the resulting relative entropy, fluctuation theorems, and Clausius-like inequality are independent of representative choice. This addition will also confirm that the results are not artifacts of any particular gauge fixing. revision: yes

Circularity Check

1 steps flagged

Entropy production identified with relative entropy by construction on gauge-reduced trajectories

specific steps
  1. self definitional [Abstract]
    "Entropy production is identified with the relative entropy between forward and backward probability measures on the gauge-reduced space of thermodynamic trajectories, revealing irreversibility as a geometric consequence of limited observability."

    The identification is stated as a consequence of the gauge construction, but relative entropy between path measures is the conventional definition of entropy production in fluctuation theorems; the gauge reduction supplies new coordinates but does not derive the functional form independently, rendering the subsequent theorems and inequalities equivalent to known results on the reduced space.

full rationale

The paper's central results (detailed FT, integrated FT, Clausius inequality, third-law limit) rest on identifying entropy production with relative entropy between forward/backward measures in the gauge-reduced space. This identification is presented as emerging from the gauge symmetry, yet it directly imports the standard definition of entropy production from stochastic thermodynamics and applies it to the new quotient space without an independent derivation of the functional form. Subsequent claims of gauge invariance and unification then follow tautologically once the standard relative-entropy expression is adopted on the reduced trajectories. No other circular steps (self-citation chains, fitted parameters, or ansatz smuggling) are evident from the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 3 invented entities

The central construction rests on treating measurement limits as a gauge symmetry and on introducing several new objects whose independent empirical status is not addressed in the abstract.

axioms (1)
  • domain assumption Measurement constraints can be modeled as a gauge symmetry acting on density operators.
    This modeling choice is stated at the outset of the abstract and is required for the subsequent reduction to a gauge-invariant space.
invented entities (3)
  • gauge-reduced space of physically distinguishable states no independent evidence
    purpose: To represent only those quantum states that remain distinguishable under the imposed measurement constraints.
    Introduced as the output of the gauge symmetry reduction; no external falsifiable signature is given in the abstract.
  • invariant entropy no independent evidence
    purpose: To provide a gauge-invariant quantity that admits a stochastic description and obeys fluctuation theorems.
    Defined within the reduced space; its properties are derived from the gauge construction rather than from prior independent evidence.
  • coherent heat no independent evidence
    purpose: To serve as one of the quantities in the unified first-and-second-law inequality.
    Appears as a new term alongside invariant work; no prior literature reference or independent test is supplied in the abstract.

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