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arxiv: 2604.24780 · v2 · pith:5KRQ6AHOnew · submitted 2026-04-20 · ⚛️ physics.gen-ph

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

Jorge Pinochet , Giorgio Sonnino This is my paper

Pith reviewed 2026-05-21 01:15 UTC · model grok-4.3

classification ⚛️ physics.gen-ph
keywords entropygravitythermodynamicssecond lawblack holesstellar contractioncore collapse
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0 comments X

The pith

Gravity preserves the second law of thermodynamics when radiation and emitted energy are included in the accounting.

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

This paper investigates if gravity violates the second law by comparing an ideal gas with and without significant gravitational effects. It concludes that local ordering from gravity, like in collapsing stars, is accompanied by entropy export through radiation, keeping the total entropy of the full system rising. The authors use straightforward calculations for the Sun, black hole limits, protostars, and supernova core collapse to illustrate this. Readers care about this because it explains how the universe develops structure without thermodynamic contradiction.

Core claim

The authors argue that gravity-induced apparent entropy reductions are illusory when the system is considered in full, as the entropy carried by outgoing radiation and particles ensures the total increases, consistent with the second law for isolated systems.

What carries the argument

Inclusion of entropy from all emitted radiation and energy to maintain the isolated system condition for applying the second law.

If this is right

  • For the Sun, radiation entropy growth dominates over any gravitational ordering effects.
  • Black hole formation at extreme contraction limits does not produce a net entropy decrease.
  • The protostellar contraction process shows increasing total entropy with energy emission.
  • Neutrino cooling in core collapse leads to overall entropy increase in the system.

Where Pith is reading between the lines

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

  • Similar entropy balancing might be relevant for understanding large-scale cosmic structure formation.
  • This view could guide analyses of entropy in other self-gravitating systems like galaxies.

Load-bearing premise

The entire gravitating object and its emitted radiation together form an isolated system to which the second law applies directly.

What would settle it

Finding a case of gravitational collapse where the entropy of the object and all its emitted radiation and particles together decreases would disprove the claim.

Figures

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

Figure 1
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. 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. 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. 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. 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.

Referee Report

1 major / 0 minor

Summary. The manuscript claims that gravity does not violate the second law of thermodynamics. Although gravitational systems can exhibit local ordering and structure formation, the second law remains valid when the composite system (matter plus all emitted radiation and energy) is treated as isolated, as illustrated conceptually through four examples: the Sun, the limit of extreme contraction in black holes, the protostellar contraction sequence, and core collapse with neutrino cooling.

Significance. If the arguments hold, the work fills a noted gap in physics education by providing a clear conceptual resolution to a common question about entropy and gravity. It emphasizes proper system boundaries and could serve as a useful classroom resource for illustrating that apparent local entropy decreases are offset globally.

major comments (1)
  1. [Abstract] Abstract: The central claim that the second law holds for the enlarged system in each of the four examples rests on the assertion that total entropy (including radiation) must increase. However, the manuscript explicitly omits the detailed calculations for these examples, providing only conceptual framing. This leaves the quantitative entropy accounting unverified and is load-bearing for the claim that no violation occurs.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation of the manuscript's educational potential and for identifying a point that can strengthen the presentation. We respond to the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the second law holds for the enlarged system in each of the four examples rests on the assertion that total entropy (including radiation) must increase. However, the manuscript explicitly omits the detailed calculations for these examples, providing only conceptual framing. This leaves the quantitative entropy accounting unverified and is load-bearing for the claim that no violation occurs.

    Authors: We agree that the manuscript emphasizes conceptual framing over exhaustive numerical entropy budgets for the four examples, consistent with its stated educational focus and the decision to omit calculations not strictly necessary for the core argument. The claims rest on standard results from stellar astrophysics and general relativity (e.g., the entropy flux carried by photons from the Sun or neutrinos in core collapse), which are known to ensure a net entropy increase for the composite system. Nevertheless, we recognize that brief order-of-magnitude estimates would make the accounting more explicit without altering the paper's scope. We will therefore revise the text to include short quantitative sketches, supported by references to established calculations, for the Sun and protostellar contraction examples while retaining the conceptual emphasis. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper applies the standard second law of thermodynamics to an enlarged isolated system that includes all emitted radiation and energy when analyzing gravitational examples such as the Sun, black holes, protostellar contraction, and core collapse. This is an external principle invoked on composite boundaries rather than a quantity redefined in terms of the target conclusion. The four representative cases use simplified conceptual arguments and basic calculations without parameter fitting, self-referential definitions, or load-bearing self-citations that reduce the central claim to its own inputs. The derivation chain therefore remains self-contained and independent of the result it seeks to illustrate.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that the second law applies to the enlarged system including radiation, with no free parameters or invented entities introduced.

axioms (1)
  • domain assumption The second law of thermodynamics holds for isolated systems, requiring total entropy to increase or stay constant.
    Invoked to conclude that apparent local decreases are compensated when the full system with radiation is considered.

pith-pipeline@v0.9.0 · 5700 in / 1116 out tokens · 39108 ms · 2026-05-21T01:15:34.940161+00:00 · methodology

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