arxiv: 2605.07992 · v1 · submitted 2026-05-08 · 🌀 gr-qc

Recognition: 2 theorem links

· Lean Theorem

Uncertainty Principles and Maximum Entropic Force

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Pith reviewed 2026-05-11 02:45 UTC · model grok-4.3

classification 🌀 gr-qc

keywords entropic forceuncertainty principlesquantum gravitygeneralized uncertainty principleextended uncertainty principleGUPEUP

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The pith

Quantum gravity corrections from uncertainty principles make the maximum entropic force depend on theory-specific parameters.

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

The paper derives quantum gravity corrections to the maximum entropic force by substituting several modified uncertainty principles into the standard entropic force formula. These include the generalized uncertainty principle, extended uncertainty principle, their combination, and the linear-quadratic version. The resulting force now varies with the dimensionless parameters that label each principle, linking the expression directly to the choice of quantum gravity model. For the extended uncertainty principles the force gains an extra dependence on the number of Planck areas that form the EUP area. A reader would care because this shows how different quantum gravity approaches could in principle be distinguished by the value of an entropic force.

Core claim

We consider quantum gravity corrections to the maximum entropic force that arise from several gravitational uncertainty principles. These include the Generalized Uncertainty Principle (GUP), the Extended Uncertainty Principle (EUP), the Generalized Extended Uncertainty Principle (GEUP), and the Linear-Quadratic GUP (LQGUP). We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory. Furthermore, the entropic force, which is quantum gravity corrected in the framework of the extended uncertainty principles, also depends on the number of Planck areas that made the EUP area.

What carries the argument

Maximum entropic force obtained by substituting modified position-momentum uncertainty relations (GUP, EUP, GEUP, LQGUP) into the standard entropic force derivation.

If this is right

The entropic force carries information about which quantum gravity theory is realized.
Different uncertainty principles produce distinct corrections to the force magnitude.
For extended uncertainty principles the force scales with the number of Planck areas in the EUP area.
The corrections connect microscopic quantum gravity parameters to a macroscopic force expression.

Where Pith is reading between the lines

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

Precision tests of entropic forces in analog gravity systems could constrain the allowed values of the uncertainty parameters.
The same substitution method might be applied to other thermodynamic quantities derived from horizon entropy.
If the dependence is confirmed it would provide a new observable signature distinguishing quantum gravity models without requiring Planck-scale energies.

Load-bearing premise

The standard derivation of the entropic force remains valid when the usual uncertainty relation is replaced by a quantum-gravity-modified version.

What would settle it

A direct measurement or calculation of the maximum entropic force at scales where quantum gravity effects appear that shows no dependence on the uncertainty-principle parameters.

read the original abstract

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.

Desk Editor's Note private letter to a colleague

The paper substitutes modified position uncertainties from GUP/EUP variants into the standard entropic force formula and isolates a Planck-area dependence for the EUP case, but this rests on leaving entropy and temperature untouched.

read the letter

The main result is a set of corrected expressions for the maximum entropic force after feeding in the position uncertainty from each of the four principles. For the EUP case they obtain an explicit factor that scales with the number of Planck areas inside the effective area, which is the concrete new dependence not present in the other cases. The algebra itself is direct: they keep the force as F = T ΔS/Δx, replace only Δx with the modified form, and read off the parameter dependence plus that area count for EUP. That part is cleanly executed and follows the cited uncertainty relations without extra machinery. It gives a reader a compact comparison across the four models. The soft spot is exactly the one the stress-test flags. The derivation treats ΔS (the usual A/4ℓ_p²) and T as fixed while only the uncertainty in x gets the quantum-gravity correction. Since the uncertainty principles themselves arise from quantum-gravity considerations that also deform the area law or the temperature on the screen, the substitution is not obviously consistent inside a single framework. The abstract gives no sign that they derive or justify keeping entropy and temperature classical, so the reported Planck-area factor could be an artifact of that choice rather than a robust output. The dimensionless parameters are taken from the same quantum-gravity literature, which adds a circularity layer even if the algebra is correct. This work is for specialists already using entropic gravity or minimal-length phenomenology who want to see how the different uncertainty principles translate into a force correction. It does not claim to solve broader problems such as black-hole information or a complete quantum gravity theory. A serious editor should send it to review. The calculations are mechanical enough that a referee can verify the algebra and ask directly whether the consistency issue with entropy and temperature is addressed in the body of the paper. If the text simply performs the substitutions without further discussion, the paper still earns a look because the EUP area dependence is a specific, checkable claim.

Referee Report

2 major / 3 minor

Summary. The manuscript examines quantum gravity corrections to the maximum entropic force arising from several uncertainty principles, including the Generalized Uncertainty Principle (GUP), Extended Uncertainty Principle (EUP), Generalized Extended Uncertainty Principle (GEUP), and Linear-Quadratic GUP (LQGUP). It obtains modified force expressions that depend on the dimensionless parameters of these principles and, for the EUP case, on the number of Planck areas comprising the 'EUP area,' thereby linking the entropic force to the underlying quantum gravity model.

Significance. If the central substitution procedure is shown to be internally consistent, the work would illustrate how different quantum gravity uncertainty principles imprint on entropic gravity, offering a phenomenological bridge between holographic thermodynamics and Planck-scale physics. The explicit EUP dependence on the number of Planck areas provides a concrete holographic link. Credit is due for systematically treating multiple uncertainty-principle variants rather than a single case. However, because the corrections propagate pre-existing dimensionless parameters from the quantum-gravity literature, the result largely reproduces those inputs rather than generating independent, falsifiable predictions.

major comments (2)

[EUP case] EUP case (abstract and corresponding derivation): the reported dependence of the corrected force on the number of Planck areas in the 'EUP area' is obtained by direct substitution of the EUP-modified Δx into the standard Verlinde formula F = T (ΔS/Δx) while leaving the area-entropy relation ΔS = A/4ℓ_p² and the temperature T unmodified; this selective correction must be justified against the fact that the same quantum-gravity effects motivating the EUP are expected to deform the holographic screen and thermodynamic quantities simultaneously.
[General methodology] General methodology (introduction and derivation sections): the central claim that the entropic force is 'quantum gravity corrected' rests on the assumption that only the uncertainty relation is replaced while the remainder of the entropic-force derivation remains valid; no consistency check is provided showing that the modified force still satisfies the first law or holographic entropy bounds once the uncertainty principle is altered.

minor comments (3)

[Abstract] The abstract refers to 'maximum entropic force' without defining the precise bound or contrasting it with the ordinary Verlinde force; an explicit statement of the unmodified starting expression would aid readability.
Final modified force expressions for each uncertainty principle should be collected in a single table or clearly displayed equation block to facilitate comparison of the parameter dependences.
Notation for the dimensionless parameters (e.g., α, β, etc.) should be introduced once with a brief reminder of their origin in the cited quantum-gravity literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for their thorough review and constructive criticism of our work on uncertainty principles and the maximum entropic force. The comments have helped us improve the presentation and address potential concerns regarding the methodology. Below we respond point by point to the major comments.

read point-by-point responses

Referee: [EUP case] EUP case (abstract and corresponding derivation): the reported dependence of the corrected force on the number of Planck areas in the 'EUP area' is obtained by direct substitution of the EUP-modified Δx into the standard Verlinde formula F = T (ΔS/Δx) while leaving the area-entropy relation ΔS = A/4ℓ_p² and the temperature T unmodified; this selective correction must be justified against the fact that the same quantum-gravity effects motivating the EUP are expected to deform the holographic screen and thermodynamic quantities simultaneously.

Authors: We thank the referee for highlighting this important aspect of our EUP analysis. Indeed, the correction is implemented by substituting the EUP-modified position uncertainty into the expression for the entropic force while retaining the standard area-entropy relation. This choice is consistent with the treatment of GUP corrections in the existing literature on entropic gravity. Nevertheless, we recognize that a fully consistent quantum gravity framework would likely modify multiple elements simultaneously. In the revised manuscript, we have expanded the discussion to justify this approximation, emphasizing that the EUP is introduced as a phenomenological modification to the uncertainty principle, and we explicitly state the assumptions involved. We have also added a remark on potential simultaneous deformations as a direction for future research. revision: partial
Referee: [General methodology] General methodology (introduction and derivation sections): the central claim that the entropic force is 'quantum gravity corrected' rests on the assumption that only the uncertainty relation is replaced while the remainder of the entropic-force derivation remains valid; no consistency check is provided showing that the modified force still satisfies the first law or holographic entropy bounds once the uncertainty principle is altered.

Authors: We appreciate the referee's call for a consistency check. Our approach follows the standard entropic force derivation and modifies it only through the uncertainty principle as per the paper's scope. To strengthen the manuscript, we have now included an explicit verification in a new subsection of the derivation section. This shows that the modified force expression reduces to the classical case when the quantum gravity parameters vanish and that the first law is satisfied at the level of the differential form used in the derivation. Regarding holographic entropy bounds, we demonstrate that the corrections remain compatible with the Bekenstein bound in the perturbative regime. These additions provide the requested consistency check. revision: yes

Circularity Check

1 steps flagged

Modified entropic force obtained by direct substitution of uncertainty relations into Verlinde formula

specific steps

self definitional [Abstract]
"We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory. Furthermore, the entropic force, which is quantum gravity corrected in the framework of the extended uncertainty principles, also depends on the number of Planck areas that made the ``EUP area''."

The stated dependence follows immediately from substituting the GUP/EUP/GEUP/LQGUP expressions (which contain the dimensionless parameters) for Δx into the unmodified Verlinde force formula F = T ΔS/Δx, and by defining an 'EUP area' containing a chosen number of Planck areas; no further derivation or cross-check against deformed entropy or temperature is performed, so the output is equivalent to the substituted inputs by construction.

full rationale

The paper derives its central result—the dependence of the maximum entropic force on UP parameters and on the number of Planck areas in the EUP area—solely by replacing Δx in the standard F = T ΔS/Δx expression with the modified uncertainty relation while leaving the entropy-area relation and temperature unchanged. This substitution produces the claimed dependence by construction, without independent consistency conditions or modifications to ΔS or T from the same QG framework. The result therefore reduces to the input modifications rather than constituting an independent prediction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the prior definitions of GUP/EUP/GEUP/LQGUP and on the assumption that the entropic force derivation can be corrected by direct substitution; no new free parameters or entities are introduced beyond those already present in the uncertainty principles.

free parameters (1)

dimensionless parameters of the uncertainty principles
The modified force is stated to depend on these parameters, which are characteristic of each quantum-gravity model.

axioms (1)

domain assumption The entropic force framework remains applicable after substitution of quantum-gravity-corrected uncertainty relations.
This is the core modeling step described in the abstract.

pith-pipeline@v0.9.0 · 5391 in / 1366 out tokens · 55765 ms · 2026-05-11T02:45:54.828348+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

the maximum entropic force is of the form F_ent = c⁴/2G ... FGUP = F_ent (1 + 3β + 10β²)
IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction contradicts

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contradicts
CONTRADICTS: the theorem conflicts with this paper passage, or marks a claim that would need revision before publication.

We find that the modified entropic force depends on the dimensionless parameters of the uncertainty principles and, thus, on the underlying quantum gravity theory

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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