Thermodynamic behavior of cosmological models with fractional entropy

arXiv:2604.17682 · gr-qc, astro-ph.CO · Submitted 2026-08-19 · Read on arXiv

Listen

Radio episode about this paper

Transcript

Introduction to the show: ident: Astrophysics Radio. Generated commentary on the latest astrophysics papers.

Vera: Next we'll be talking about the paper "Thermodynamic behavior of cosmological models with fractional entropy".

Jocelyn: The paper was written by Miguel Cruz, Diego da Silva, Simón González, Samuel Lepe, Joel Saavedra et al. from University of Veracruz (Facultad de Fı́sica) and Pontifical Catholic University of Valparaíso (Instituto de Fí́sica) and University of Playa Ancha (Laboratorio de investigación de Cómputo de Física, Facultad de Ciencias Naturales y Exactas).

Vera: Stay tuned as we take you through the paper and discuss its implications.

Title: Vera: So, we're starting out by looking at the title again: "Thermodynamic behavior of cosmological models with fractional entropy." This tells us immediately that the core focus isn't just on the math, but on how this new physics impacts thermodynamics.

Jocelyn: It’s interesting that they are applying this concept to the *apparent* horizon of a flat Friedmann-Lemaître-Robertson-Walker universe, which is a standard way we model our cosmos. What does focusing on that specific boundary reveal?

Subrahmanyan: The apparent horizon acts like a thermal system, and by forcing it to obey thermodynamic laws, the authors are seeing what happens when that boundary isn't behaving according to Bekenstein-Hawking rules. It’s about probing the fundamental degrees of freedom of spacetime.

Vera: It seems like they are trying to see if this fractional approach offers a more stable alternative than some of the dark energy models we’ve seen previously, where things can get quite wild.

Jocelyn: That's what I'm hoping to hear about—whether this complex parameter alpha is leading us toward a smooth and predictable expansion history, Subrahmanyan.

Subrahmanyan: The fractional nature suggests a kind of structural irregularity in spacetime that might actually be very stable, which is a huge relief for our cosmological models. It’s about finding continuity where we might have previously seen instabilities.

Summary/Findings: Vera: Moving into the summary of the paper, they present some key results that are quite reassuring regarding stability. They found that the specific heats, C V and C P, share a consistent sign across time.

Jocelyn: That’s a massive finding for us observers! If those heat capacities never change signs or diverge, it means the model avoids what we call pathological phase transitions, right?

Subrahmanyan: Precisely. The mathematical structure of fractional entropy prevents those sudden, catastrophic shifts that plague some alternative dark energy scenarios. The system remains thermodynamically well-behaved and smooth during the accelerated expansion epoch.

Vera: And they did this by using a unified first law of thermodynamics to derive their modified Friedmann equations, which is a very elegant way to tie the thermal properties directly into the geometry of space.

Jocelyn: So, even if alpha is not exactly two we still have a coherent picture of how matter and energy are moving through space. How does this look when they compare it to real-world data?

Subrahmanyan: The paper shows that the model fits our current observational data—things like Cosmic Chronometers, Pantheon+, and DESI DR2—much better than expected if we’re using the traditional approach. It's a strong case for a finding that is both theoretically sound and observable.

Improvements/Next Steps: Vera: We’ve seen that this model is stable, but now let’s talk about how it changes the actual expansion of the universe. The paper shows that alpha isn' to be just a parameter; it actively modulates the background dynamics.

Jocelyn: That’s what I'm interested in—the way H zero, our Hubble constant, and m0, the density of matter, shift depending on this fractional parameter. Does that mean we can use alpha to distinguish between different expansion histories?

Subrahmanyan: Absolutely. The paper demonstrates that decreasing the value of alpha shifts H zero upward and lowers the matter density, which is a very clear, predictable pattern. This makes alpha a powerful tool for comparing observational constraints against traditional cosmology.

Vera: It suggests that instead of just accepting one fixed value for alpha, we can have a range of possibilities that still fit the data. The results show that the data strongly prefer values close to two, which is our standard General Relativity limit.

Jocelyn: That’s a huge piece of information for us in the sky surveys; knowing that alpha is close to two gives us confidence in our current models while still allowing for a tiny bit of room for improvement.

Subrahmanyan: The fact that the fit quality degrades as alpha moves away from two confirms this—the observational data really favor the traditional approach, but the fractional model allows us to explore deviations that are physically significant.

Conclusion: Vera: To wrap up our discussion on "Thermodynamic behavior of cosmological models with fractional entropy," we’ve seen how this work fundamentally changes our view of spacetime thermodynamics.

Jocelyn: We learned that by replacing the standard area law with a fractional entropy, the universe doesn't become pathologically unstable, which is a massive relief for us observers.

Subrahmanyan: I think it's important to highlight that this isn't just a theoretical exercise; it provides a viable, stable framework that is compatible with our most precise late-time observational data.

Vera: We saw the power of testing this model against CC, Pantheon+, SH0ES, and DESI DR2, showing how the fractional parameter alpha acts as a subtle dial for H zero and m0.

Jocelyn: It’s clear that while the fractional framework is robust and consistent with current observations, it opens up new avenues to see if we can break those degeneracies between parameters.

Subrahmanyan: And I hope future studies into the formation of large-scale structures will use this same tools to test if we can distinguish these fractional degrees of freedom from standard Lambda-CDM.

Vera: That's a great way to end things, Subrahmanyan, by looking forward to the next big observational challenges.

Jocelyn: We appreciate all the insights today and the work of the team behind "Thermodynamic behavior of cosmological models with fractional entropy."

Miguel Cruz, Diego da Silva, Simón González, Samuel Lepe, Joel Saavedra, Manuel Gonzalez-Espinoza

University of Veracruz (Facultad de Fı́sica) · Pontifical Catholic University of Valparaíso (Instituto de Fí́sica) · University of Playa Ancha (Laboratorio de investigación de Cómputo de Física, Facultad de Ciencias Naturales y Exactas)

gr-qc, astro-ph.CO

Submitted: 2026-08-19

Updated: 2026-08-20

Comments: 17 pages, 6 figures. Published version in Nucl. Phys. B

Journal ref: Nucl. Phys. B 1030, 117616 (2026)

DOI: 10.1016/j.nuclphysb.2026.117616

Code: https://github.com/CobayaSampler/bao_data

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Importance score: 87/100

The gist: The study investigates "the thermodynamic and phenomenological implications of a cosmological model governed by fractional entropy applied to the apparent horizon of a flat

Key concepts

Apparent Horizon
The apparent horizon is a specific boundary used in cosmological modeling. It acts as a thermal system, and by forcing it to obey thermodynamic laws, researchers can probe the fundamental degrees of freedom of spacetime and see how it behaves when deviating from standard Bekenstein-Hawking rules.
Fractional Entropy
This concept involves using a fractional approach to model spacetime. It allows for structural irregularity that is stable, providing a reliable alternative to some dark energy models that previously showed instability or wild behavior in cosmological predictions.

Terminology

Summary

The study investigates the thermodynamic and phenomenological implications of a cosmological model governed by fractional entropy applied to the apparent horizon of a flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. The objective is to analyze how modifying the fundamental scaling of entropy affects the macroscopic gravitational dynamics and the observable expansion history of the cosmos.

Thermodynamic Framework and Stability Analysis

The researchers utilize the unified first law of thermodynamics alongside the Kodama-Hayward temperature to derive a generalized set of Friedmann equations. The core modification lies in replacing standard Bekenstein–Hawking entropy with a fractional form, S alpha. A common definition is given as:

S alpha = gamma A alpha, (1)

where gamma is a normalization constant, and A is the horizon area. While alpha = 1 recovers the standard Bekenstein–Hawking entropy, deviations from this value encode new scaling regimes that may arise if spacetime has a fractal-like microstructure or if the underlying statistical mechanics deviates from the Boltzmann–Gibbs paradigm.

The analysis of the unified first law (UFL), dE = T h dS h + W dV, leads to a specific thermodynamic conclusion: "the thermodynamic analysis reveals that the specific heats C V and C p share the same sign and depend solely on the deceleration parameter, demonstrating that the fractional model is thermodynamically stable during the late-time accelerated expansion and does not exhibit phase transitions. This stability is crucial, as it ensures a smooth, continuous modification" of cosmic evolution.

Modified Cosmological Dynamics

The application of this fractional entropy results in modified Friedmann equations. The authors distinguish between the general case and the truncated fractional model, which occurs when (alpha) = 0 (or =2). The truncated Friedmann equation is presented as:

squared + k over a squared over 8 pi = rho, (33)

The full set of equations, incorporating the fractional parameter alpha, are given by:

(squared + (alpha) H squared over 8 pi. [and similar terms] = rho, (19)

Observational Constraints and Parameter Fitting

The model is tested against a joint sample of late-time observational data, including Cosmic Chronometers, Pantheon+SH0ES supernovae, and the latest DESI DR2 Baryon Acoustic Oscillations.

  1. Fit Quality: The researchers found that in the "physically motivated range 1 < alpha 2, we find that the fit quality degrades monotonically as alpha decreases from the General Relativity limit."

  2. Parameter Shifts: The fractional parameter alpha acts as a physically relevant degree of freedom that modulates expansion. Specifically, decreasing alpha coherently shifts H 0 upward and m0 downward, revealing that the fractional parameter modulates the background expansion in a physically nontrivial and observationally distinguishable way.

  3. Best-Fit Results: The full MCMC analysis yields specific values for the parameters:

  • H 0 = 69.50 plus or minus 0.42 km/s/Mpc (at alpha = 2).

  • m0 = 0.292 plus or minus 0.008 (at alpha = 2).

Conclusion

The study concludes that the fractional entropy model is fully compatible with current observational constraints, achieving a level of precision comparable to the standard CDM model (chi 2 nu about 0.886). The statistical analysis confirms that while the parameter space is bounded, the data favor values of alpha close to 2.

Improvements for AI systems

Based on a rigorous analysis of this scientific paper, the following specific improvements can be implemented into advanced AI research and data analysis systems:

  1. Implementation of Non-Additive Entropy Dynamics: The AI system can now incorporate the fractional entropy functional (S alpha) as a fundamental component of its cosmological models, moving beyond standard Bekenstein-Hawking scaling (S=A/4). This allows the the AI to simulate universes where microstate statistics are fundamentally altered by non-additivity.

  2. Full Thermodynamic Modeling: The AI can execute simulations based on the Unified First Law (UFL) (dE = T H dS H + W dV) coupled with the Kodama-Hayward temperature, providing a complete thermodynamic description of the apparent horizon, rather than treating energy density and expansion independently.

3 Automated Friedmann Equation Solving: The AI can solve the complex system of modified Friedmann equations (Equations 19 and 20) in a closed form, allowing it to accurately predict H(z) for any given a alpha and set initial conditions, without relying on simplified CDM approximations.

  1. Multi-Probe Joint Likelihood Calculation: The AI can perform automated Bayesian inference by simultaneously calculating the total chi-square function (chi 2 tot) across four distinct observational datasets:

  • Cosmic Chronometers (CC): Estimating H(z) from galaxy age evolution.

  • Type Ia Supernovae (SNe Ia): Calculating chi 2 SN based on the distance modulus (mu) and incorporating the full covariance matrix (C).

  • DESI DR2 BAO: Quantifying chi 2 DESI using both transverse and radial distance indicators (D M, D H, D V).

  • SH0ES Prior: Integrating the specific local H 0 measurement.

  1. Quantified Degeneracy Mapping: The AI can precisely map and track the strong anti-correlation between H 0 and m0 as a function of alpha. It will not only identify this degeneracy but also allow for the systematic exploration of the parameter space where decreasing alpha leads to a quantifiable shift in both H 0 (upward) and m0 (downward).

  2. Constraint Extraction: The AI can reliably extract the statistically robust constraints on alpha from MCMC sampling, specifically identifying the strong preference for the upper bound (alpha about 2) while providing a precise lower bound (1.92 alpha 2.00 at 68% CL).

  3. Automated Stability Diagnostics: The AI can perform instant thermodynamic stability checks on the model by analyzing the behavior of the specific heats (C V and C p). It will automatically confirm that:

  • C V(t) and C p(t) share a common positive sign.

  • The model strictly avoids divergences or sign changes, ensuring no horizon phase transitions occur.

  1. Deceleration Parameter Prediction: The AI can simulate the evolution of the deceleration parameter q(z) for any alpha, accurately predicting:

  • The transition redshift (z t) where q(z) crosses zero.

  • The present-day value of q 0 (e.g, predicting a more negative q 0 as alpha decreases).

  1. Relative Deviation Quantification: The AI can calculate the percentage deviation (mu(%)) between the fractional model's predicted luminosity distance (mu frac) and the standard CDM prediction (mu CDM), allowing it to quantify exactly how much a given alpha deviates from the concordance model at specific redshifts.

Sources

Related papers