arxiv: 2604.24780 · v1 · submitted 2026-04-20 · ⚛️ physics.gen-ph

Recognition: unknown

Entropy, Gravity, and an Apparent Violation of the Second Law

Jorge Pinochet , Giorgio Sonnino

Authors on Pith no claims yet

Pith reviewed 2026-05-10 03:51 UTC · model grok-4.3

classification ⚛️ physics.gen-ph

keywords entropygravitysecond law of thermodynamicsblack holesstar formationradiationthermodynamics

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The pith

Gravity does not violate the second law when the full system and all its emitted radiation are accounted for.

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

The paper asks whether gravity can break the second law of thermodynamics through the formation of ordered structures. It compares an ideal gas with negligible gravity to the same gas under strong gravitational influence. Local entropy drops occur during collapse and structure formation, yet the total entropy of the entire system rises once the entropy carried by all radiated energy is included. This result is shown through four simple cases: the Sun, the final contraction to a black hole, protostellar collapse, and core collapse cooled by neutrinos. The work argues that standard textbook treatments miss this conclusion because they omit the entropy of the outgoing radiation.

Core claim

Although gravity can produce local ordering and apparent entropy decreases in parts of a system, the second law remains valid for the complete isolated system when every form of emitted energy and radiation is counted in the entropy balance. In the Sun, radiation carries away enough entropy to offset any local ordering. The same compensation occurs in the limit of black-hole formation, during protostellar contraction, and in neutrino-cooled core collapse. Simple calculations without full derivations suffice to demonstrate the net entropy increase in each case.

What carries the argument

The total entropy balance obtained by adding the entropy of all emitted radiation and energy to the entropy change inside the gravitating system itself.

If this is right

Local entropy decreases during gravitational collapse are always more than offset by entropy exported in radiation.
The second law holds without exception for the Sun when its total radiated output is included.
Extreme gravitational contraction down to black-hole densities produces no net entropy violation.
Protostellar contraction and neutrino-cooled core collapse both exhibit overall entropy growth when radiation is counted.
Textbook discussions of entropy and gravity must incorporate the entropy of outgoing energy to avoid apparent paradoxes.

Where Pith is reading between the lines

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

The same accounting would apply to galaxy formation, where light and heat radiated by stars must be added to the entropy budget of the forming structure.
Numerical simulations of gravitational collapse could routinely track radiation entropy to confirm consistency with the second law at every step.
Astronomical observations of the entropy carried by supernova ejecta and neutrinos could provide direct empirical checks on these balances.

Load-bearing premise

That the entire system plus all radiation it emits can be treated as an isolated system for applying the second law.

What would settle it

A concrete measurement showing that the combined entropy of a collapsing star and all radiation it has emitted over time is lower than at the start would disprove the central claim.

Figures

Figures reproduced from arXiv: 2604.24780 by Giorgio Sonnino, Jorge Pinochet.

**Figure 1.** Figure 1: Free expansion of an ideal gas. Entropy increases as the gas expands. Since the gas is ideal, the internal energy U depends only on temperature: U = U(T), and there are no interparticle potentials. No external work is done (expansion occurs in a vacuum), no heat flows, we have: δQ = 0, δW = 0 (1) Energy balance for the isolated gas reads: ∆U = Q − W = 0 − 0 = 0 (2) For an ideal gas U = U(T), so ∆U = 0 ⇒ ∆T… view at source ↗

**Figure 2.** Figure 2: A mass M of ideal gas with a spherical shape, composed of N particles of mass m that move randomly and are held together by the attraction they exert on each other. We will demonstrate this explicitly by writing down the energy conservation law, expressing the rate of entropy change of the gas and the radiation, and combining them to obtain a manifestly non-negative total entropy production under the stand… view at source ↗

**Figure 3.** Figure 3: Free contraction of an ideal gas. The increase in entropy is associated with a reduction in the volume and uniformity of the gas distribution. Note the inverse dependence on R: a contraction (R ↓) implies heating (T ↑). This is the origin of negative heat capacity in self-gravitating systems [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

**Figure 4.** Figure 4: By combining the rate of entropy change of the gas and the radiation, we get a non-negative total entropy production under the standard physical assumptions (quasi-static contraction and radiation leaving the system). The compensating entropy is carried away by the emitted energy (photons, neutrinos, gravitational waves, etc.). 7 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗

**Figure 5.** Figure 5: is as follows: (I) the gas mass contracts and heats, emitting thermal radiation; (II) A black hole is formed, which we can assume initially absorbs everything contained in the vessel, including the radiation emitted during phase I; (III) The black hole evaporates completely, and inside the container, there is only Hawking radiation [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

read the original abstract

An interesting question to explore in physics classes is whether gravity violates the second law of thermodynamics. Standard physics textbooks provide little to no discussion of the relationship between entropy and gravity, and the same is often true of specialized texts. The aim of this work is to address this question by analyzing the behavior of an ideal gas in two simple scenarios: one in which gravity is negligible and another in which its effects are significant. We show that although systems influenced by gravity may exhibit counterintuitive behavior, such as local ordering through structure formation, the second law of thermodynamics remains valid when the entire system is considered, including all emitted energy and radiation. Given the educational focus of this work and the complexity of the entropy-gravity relationship, we omit detailed calculations that are not strictly necessary and instead focus on the simplest physical scenarios. In this context, we analyze four representative examples through simple calculations: the Sun, the limit of extreme contraction in black holes, the protostellar contraction sequence, and core collapse with neutrino cooling.

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

This is a classroom note restating the standard fix for the gravity-entropy puzzle, but it leaves out the calculations it says it performs.

read the letter

The punchline is that this is an educational clarification on entropy and gravity rather than a new result. The authors argue that local ordering from gravity is offset by entropy in emitted radiation, using four examples, but they leave out the actual calculations. It does a reasonable job framing the question for a physics class setting. The discussion of the ideal gas in gravity versus no gravity sets up the counterintuitive part nicely, and the examples span everyday astrophysics to extreme cases. The soft spots are in the execution. The paper states that it performs simple calculations for the Sun, black hole limits, protostellar sequence, and neutrino-cooled collapse, yet omits the details. This makes it impossible to verify the entropy accounting. Standard ways to compute this would involve the entropy of the gas, the gravitational potential energy contribution if treated thermodynamically, and the entropy of the radiated energy, but none of that is shown. The claim therefore rests on qualitative reasoning alone. There is nothing new in the conclusion. The idea that the second law holds for the whole system including radiation is textbook material in stellar structure and cosmology. This paper is for instructors or advanced students who want illustrative cases to discuss the second law in gravitational contexts. It could serve as a starting point for classroom exercises if the calculations were filled in. I would not send it for peer review. The omitted calculations are a real gap for a piece that positions itself around those calculations, and the lack of novelty means it does not need formal refereeing.

Referee Report

2 major / 1 minor

Summary. The paper claims that gravity does not violate the second law of thermodynamics. By comparing an ideal gas with and without significant gravitational effects, and by analyzing four examples (the Sun, extreme black-hole contraction, protostellar contraction sequence, and neutrino-cooled core collapse) via simple calculations, it argues that local entropy decreases from structure formation are offset by entropy increases in the emitted radiation and energy when the full system is treated as isolated.

Significance. If the entropy accounting were explicitly verified, the work could serve as a useful pedagogical clarification of how the second law applies to self-gravitating systems, addressing a frequent classroom question. As written, however, the educational value is undercut by the absence of the supporting calculations.

major comments (2)

[Abstract] Abstract: The central claim that 'the second law of thermodynamics remains valid when the entire system is considered, including all emitted energy and radiation' rests on omitted 'simple calculations' for the four examples. Without explicit entropy balances (e.g., Sackur-Tetrode term for the gas, gravitational binding-energy contribution, and photon entropy (4/3)aVT^3 for radiated energy), it is impossible to confirm that total entropy is non-decreasing in each case.
[Sun and protostellar examples] Section on the Sun and protostellar sequence: The manuscript asserts that local ordering is compensated globally, yet provides only qualitative statements rather than the quantitative comparison of initial and final total entropies. This omission is load-bearing because the examples are presented as the concrete demonstration that the second law holds.

minor comments (1)

[Abstract] The abstract refers to 'two simple scenarios' for an ideal gas but then analyzes four distinct examples; a brief roadmap linking the general argument to the specific cases would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the presentation for an educational audience. We agree that the manuscript would benefit from greater explicitness in the entropy calculations and have revised it accordingly to include the supporting quantitative details.

read point-by-point responses

Referee: [Abstract] Abstract: The central claim that 'the second law of thermodynamics remains valid when the entire system is considered, including all emitted energy and radiation' rests on omitted 'simple calculations' for the four examples. Without explicit entropy balances (e.g., Sackur-Tetrode term for the gas, gravitational binding-energy contribution, and photon entropy (4/3)aVT^3 for radiated energy), it is impossible to confirm that total entropy is non-decreasing in each case.

Authors: We appreciate this observation. The original manuscript deliberately omitted lengthy derivations to maintain focus on the core physical insight for classroom use, as the calculations rely on standard expressions. In the revision we have added an appendix with the explicit entropy balances for all four examples. These employ the Sackur-Tetrode formula for the ideal-gas entropy, include the (negative) contribution from gravitational binding energy, and use the photon entropy (4/3)aVT^3 for the radiated energy. The tabulated results confirm that the net entropy of the closed system (matter plus radiation) increases in every case. revision: yes
Referee: [Sun and protostellar examples] Section on the Sun and protostellar sequence: The manuscript asserts that local ordering is compensated globally, yet provides only qualitative statements rather than the quantitative comparison of initial and final total entropies. This omission is load-bearing because the examples are presented as the concrete demonstration that the second law holds.

Authors: We agree that quantitative verification strengthens the argument. The revised manuscript now contains explicit initial-to-final entropy comparisons for the Sun (luminosity-driven radiation entropy versus gravitational contraction) and the protostellar contraction sequence. In both cases the entropy exported by radiation exceeds the local decrease associated with structure formation, with the numerical differences shown in the new appendix. Parallel quantitative checks are supplied for the black-hole and neutrino-cooled-collapse examples as well. revision: yes

Circularity Check

0 steps flagged

No circularity; standard thermodynamic principles applied without reduction to inputs

full rationale

The manuscript applies the second law to gravitational systems by considering the total entropy of the isolated system including emitted radiation and energy. It uses qualitative arguments and simple calculations for four examples (Sun, black-hole limit, protostellar sequence, neutrino-cooled collapse) without providing or relying on fitted parameters, self-definitional equations, or load-bearing self-citations. No equations are presented that equate a derived quantity to its own input by construction, and the central claim rests on established thermodynamic accounting rather than renaming known results or smuggling ansatzes. The omission of detailed derivations is noted but does not create circularity, as the logic follows directly from standard isolated-system entropy increase without self-referential closure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper rests on standard thermodynamic and gravitational assumptions without introducing new free parameters or entities; full text unavailability limits precise enumeration.

axioms (2)

domain assumption The second law of thermodynamics holds for systems that include all emitted radiation and energy as part of the total.
Invoked to resolve apparent local entropy decreases in gravitational collapse.
domain assumption Local ordering due to gravity is always accompanied by entropy export via radiation.
Central premise for the four example scenarios.

pith-pipeline@v0.9.0 · 5469 in / 1212 out tokens · 55809 ms · 2026-05-10T03:51:30.450102+00:00 · methodology

discussion (0)

Reference graph

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