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arxiv: 2510.12863 · v2 · submitted 2025-10-14 · 🌀 gr-qc

Generalized Second Law and Thermodynamical Aspects of f(Q,mathcal{T}) Gravity

Anirudh Pradhan , A. Husain , M. Zeyauddin , S. H. Shekh This is my paper

Pith reviewed 2026-05-18 07:37 UTC · model grok-4.3

classification 🌀 gr-qc
keywords f(Q,T) gravitygeneralized second lawapparent horizonFLRW cosmologythermodynamicsmodified gravitycosmic acceleration
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The pith

In f(Q,T) gravity, linear and mildly nonlinear models satisfy the generalized second law at the apparent horizon of a flat FLRW universe, while strongly nonlinear models require parameter tuning.

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

This paper checks whether different versions of f(Q,T) gravity, a modification of general relativity that uses the non-metricity scalar and the trace of the energy-momentum tensor, obey the laws of thermodynamics during cosmic expansion. The authors apply the Gibbs relation to derive how total entropy changes at the apparent horizon and test the generalized second law for linear, power-law, quadratic, exponential, and cross-coupling forms of the function. Linear and mildly nonlinear choices generally keep entropy from decreasing, while strongly nonlinear or interaction forms need special parameter values to stay consistent. Thermodynamic checks of this kind can therefore serve as a filter for which modified gravity models remain plausible explanations for late-time acceleration.

Core claim

By applying the Gibbs relation to the apparent horizon in a flat FLRW universe, the rate of change of total entropy is calculated for several f(Q,T) models. Linear and mildly nonlinear models generally satisfy the generalized second law, whereas strongly nonlinear or cross-coupling models require fine-tuned parameters to ensure the entropy does not decrease.

What carries the argument

The rate of total entropy change at the apparent horizon, obtained via the Gibbs relation, which is used to test whether each functional form of f(Q,T) obeys the generalized second law.

If this is right

  • Linear f(Q,T) models remain viable for describing cosmic acceleration without thermodynamic inconsistency.
  • Mildly nonlinear models stay consistent provided their parameters avoid extreme values.
  • Strongly nonlinear or interaction-type models are viable only after parameter tuning that enforces positive entropy production.
  • Thermodynamic viability at the apparent horizon supplies an independent test that can narrow the space of acceptable modified gravity functions.

Where Pith is reading between the lines

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

  • If the apparent-horizon approach extends to other horizons, thermodynamic consistency could constrain f(Q,T) parameters using future large-scale structure data.
  • Models that pass this test might be prioritized for detailed comparison with supernova or CMB observations.
  • The same entropy-change method could be applied to other modified-gravity theories that incorporate non-metricity or trace terms to rank their viability.

Load-bearing premise

The standard Gibbs relation and usual thermodynamic quantities at the apparent horizon remain valid when applied inside this modified gravity theory.

What would settle it

A direct calculation for any linear f(Q,T) model that produces a negative rate of total entropy change at the apparent horizon would show the generalized second law does not hold.

read the original abstract

Late-time cosmic acceleration has motivated the exploration of various extensions of general relativity, among which $f(Q,\mathcal{T})$ gravity, based on the non-metricity scalar $Q$ and the trace of the energy--momentum tensor $\mathcal{T}$, has gained increasing attention. In this study, we explore the thermodynamic aspects of $f(Q,\mathcal{T})$ gravity by establishing the first law and generalized second law of thermodynamics at the apparent horizon of a flat FLRW universe. By applying the Gibbs relation, we determined the rate of change of the total entropy and assessed the conditions under which the generalized second law remains valid for various choices of $f(Q,\mathcal{T})$. Our analysis focuses on linear, power-law, quadratic trace, exponential, and cross-coupling models, inspired by frameworks such as $f(R,\mathcal{T})$, $f(T)$, and modifications motivated by string theory. Our analysis showed that linear and mildly nonlinear models are generally thermodynamically consistent, whereas strongly nonlinear or interaction-type models require fine-tuned parameters for the generalized second law to hold. The present analysis underscores that thermodynamic considerations serve as effective criteria for assessing the viability of modified gravity models and their relevance to cosmological dynamics.

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 manuscript investigates thermodynamic aspects of f(Q, T) gravity in a flat FLRW universe by deriving the first law and generalized second law (GSL) at the apparent horizon. It substitutes the modified Friedmann equations obtained from the f(Q, T) action into the standard Gibbs relation dE = T dS + W dV, with horizon quantities T = 1/(2π r_A) and S = A/4 where r_A = 1/H, and evaluates the sign of d(S_m + S_h)/dt for linear, power-law, quadratic, exponential, and cross-coupling models of f(Q, T). The central conclusion is that linear and mildly nonlinear models satisfy the GSL under broad conditions while strongly nonlinear or interaction-type models require fine-tuned parameter values.

Significance. If the thermodynamic framework is justified, the work supplies a concrete viability filter for f(Q, T) models that complements dynamical and observational tests, extending the thermodynamic approach already used in f(R, T) and f(T) gravity to the non-metricity-plus-trace sector. Explicit model-by-model conditions on the GSL could help narrow the large parameter space of symmetric teleparallel extensions.

major comments (2)
  1. [§3] §3: The first law and GSL are obtained by inserting the modified Friedmann equations into the unmodified Gibbs relation dE = T dS + W dV evaluated at r_A = 1/H with the standard Bekenstein-Hawking entropy S = A/4 and temperature T = 1/(2π r_A). No derivation from the f(Q, T) action is provided to confirm that the explicit T-dependence or non-metricity sector does not generate additional entropy-production terms or corrections to the heat flux proportional to f_T or Q-derivatives; if such corrections exist, the positivity conditions derived for the linear versus strongly nonlinear models in §4 would change.
  2. [§4] §4 (strongly nonlinear and cross-coupling cases): The reported GSL validity requires post-hoc adjustment of free parameters in the f(Q, T) functions so that d(S_m + S_h)/dt ≥ 0. This procedure makes the thermodynamic consistency depend on parameter selection rather than an independent prediction, weakening the claim that thermodynamic considerations serve as an effective viability criterion for these models.
minor comments (2)
  1. The introduction and §2 would benefit from explicit comparison with the thermodynamic derivations already performed for f(R, T) and f(Q) gravity to clarify the incremental contribution of the present f(Q, T) analysis.
  2. [§4] Notation for the free coefficients in the various f(Q, T) ansätze is introduced inconsistently across the model subsections; a single table collecting the functional forms and parameter ranges would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of the manuscript and the constructive comments, which have helped clarify the scope and limitations of our thermodynamic analysis. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3: The first law and GSL are obtained by inserting the modified Friedmann equations into the unmodified Gibbs relation dE = T dS + W dV evaluated at r_A = 1/H with the standard Bekenstein-Hawking entropy S = A/4 and temperature T = 1/(2π r_A). No derivation from the f(Q, T) action is provided to confirm that the explicit T-dependence or non-metricity sector does not generate additional entropy-production terms or corrections to the heat flux proportional to f_T or Q-derivatives; if such corrections exist, the positivity conditions derived for the linear versus strongly nonlinear models in §4 would change.

    Authors: We thank the referee for this important observation. Our derivation follows the standard procedure used in the literature for apparent-horizon thermodynamics in modified gravity, including f(R, T) and f(T) theories, in which the modified Friedmann equations are substituted into the usual Gibbs relation with Bekenstein-Hawking entropy and Hawking temperature. A first-principles derivation of possible additional entropy-production terms arising directly from the f(Q, T) action would be desirable; however, such an analysis is technically involved and has not been carried out even for closely related models. In the revised manuscript we have added a short clarifying paragraph at the beginning of Section 3 that explicitly states the assumptions of the present approach, references the analogous treatments in f(R, T) and f(T) gravity, and notes that potential corrections proportional to f_T or Q-derivatives remain an open question for future work. This addition provides context without altering the model-specific positivity conditions reported in §4. revision: partial

  2. Referee: [§4] §4 (strongly nonlinear and cross-coupling cases): The reported GSL validity requires post-hoc adjustment of free parameters in the f(Q, T) functions so that d(S_m + S_h)/dt ≥ 0. This procedure makes the thermodynamic consistency depend on parameter selection rather than an independent prediction, weakening the claim that thermodynamic considerations serve as an effective viability criterion for these models.

    Authors: We agree that the generalized second law holds for the strongly nonlinear and cross-coupling models only within restricted ranges of the free parameters. This parameter dependence is not introduced after the fact but emerges directly from the evaluation of d(S_m + S_h)/dt and is already stated in the original conclusions. In the revised version we have expanded the discussion in the final section to emphasize that these thermodynamic constraints function as an additional viability filter that can be combined with dynamical and observational tests to narrow the parameter space, particularly for interaction-type models. For the linear and mildly nonlinear cases the GSL is satisfied over broad intervals without fine-tuning, reinforcing the utility of the thermodynamic criterion. We believe this nuanced presentation strengthens rather than weakens the overall claim that thermodynamics provides a useful selection tool for f(Q, T) models. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation applies standard thermodynamic relations to modified Friedmann equations

full rationale

The paper establishes the first law and GSL by substituting the f(Q,T)-modified Friedmann equations into the standard Gibbs relation dE = T dS + W dV evaluated at the apparent horizon, using the usual T = 1/(2π r_A) and S = A/4. This produces model-dependent conditions on the sign of d(S_m + S_h)/dt. No step reduces by construction to a self-definition, a fitted parameter renamed as prediction, or a load-bearing self-citation chain; the fine-tuning noted for strongly nonlinear models is an explicit viability filter rather than an implicit re-derivation of the input. The central claim therefore retains independent content once the (standard but unverified) assumption that the Clausius relation remains form-invariant is granted.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central results rest on standard cosmological assumptions and thermodynamic relations plus free parameters inside the chosen f(Q,T) functions; no new entities are postulated.

free parameters (1)
  • coefficients in f(Q,T) models
    Linear, power-law, quadratic, exponential and cross-coupling forms contain adjustable constants that are selected or tuned to satisfy the generalized second law.
axioms (2)
  • domain assumption flat FLRW metric describes the universe
    Invoked to define the apparent horizon and apply thermodynamic laws in a homogeneous isotropic setting.
  • domain assumption Gibbs relation governs entropy change
    Used to compute the rate of change of total entropy at the apparent horizon.

pith-pipeline@v0.9.0 · 5758 in / 1288 out tokens · 36851 ms · 2026-05-18T07:37:39.842510+00:00 · methodology

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