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arxiv: 2605.31233 · v1 · pith:W6DJF7G4new · submitted 2026-05-29 · ❄️ cond-mat.stat-mech

Global thermodynamics for heat-conducting fluids under weak gravity

Naoko Nakagawa , Shin-ichi Sasa This is my paper

Pith reviewed 2026-06-28 20:09 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech
keywords global thermodynamicsheat conductionliquid-gas coexistenceeffective gravityvariational free energynonequilibrium thermodynamicsvan der Waals model
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The pith

The free-energy decomposition shows effective gravity governs liquid-gas transitions under heat conduction while residual heat term ensures consistency.

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

The paper establishes a global thermodynamic description for liquid-gas systems under both gravity and heat conduction by building a variational free-energy function at fixed global temperature. This function splits into a configurational component that matches the equilibrium weak-gravity form but uses an effective gravity to decide the stable arrangement of separated phases, and a residual component from excess latent heat due to conduction. The configurational part alone selects between arrangements, yet the residual part is essential for obtaining the fundamental thermodynamic relation and computing quantities such as average pressure in lab coordinates. The residual contribution further modifies the shape of barriers and interfaces in the free-energy landscape. This matters for extending thermodynamics to steady states with flows, as it predicts observable effects testable in experiments with van der Waals fluids.

Core claim

We construct a variational free-energy function for the fixed-global-temperature description and decompose it into two parts. The first has the same configurational form as the equilibrium weak-gravity free energy with gravity replaced by the effective gravity, and it determines the first-order configurational transition between the two separated liquid-gas arrangements. The second is a residual excess-latent-heat contribution that vanishes without heat conduction. Although it does not decide which separated liquid-gas arrangement is thermodynamically favored, this residual part is needed to derive the fundamental relation in the laboratory variables and to recover thermodynamic observables

What carries the argument

The decomposition of the variational free-energy function into a configurational part using effective gravity and a residual excess-latent-heat part.

If this is right

  • The first-order transition between liquid-gas arrangements is controlled by effective gravity.
  • Thermodynamic observables including spatially averaged pressure require the residual contribution for correct recovery.
  • The residual term modifies the geometry of barriers, ridges, valleys, and interfaces in the free-energy landscape.
  • Van der Waals model calculations illustrate the altered landscape under heat conduction.
  • Experimental setups can detect effective-gravity inversion at accessible scales.

Where Pith is reading between the lines

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

  • The framework could apply to other gradient-driven phase separations beyond gravity.
  • Measuring pressure averages might distinguish the residual contribution experimentally.
  • The landscape changes could affect nucleation rates or interface dynamics in heat-conducting systems.
  • Extensions to stronger gravity or different fluids may reveal further nonequilibrium effects.

Load-bearing premise

The variational free-energy function for the fixed-global-temperature description can be decomposed into the configurational part with effective gravity and the residual excess-latent-heat contribution that vanishes without heat conduction.

What would settle it

Observation of whether the spatially averaged pressure in a heat-conducting fluid under gravity matches the value predicted only when the residual excess-latent-heat term is included in the free-energy derivation.

read the original abstract

We study liquid-gas coexistence under gravity and heat conduction from the viewpoint of global thermodynamics. We construct a variational free-energy function for the fixed-global-temperature description and decompose it into two parts. The first has the same configurational form as the equilibrium weak-gravity free energy with gravity replaced by the effective gravity, and it determines the first-order configurational transition between the two separated liquid-gas arrangements. The second is a residual excess-latent-heat contribution that vanishes without heat conduction. Although it does not decide which separated liquid-gas arrangement is thermodynamically favored, this residual part is needed to derive the fundamental relation in the laboratory variables and to recover thermodynamic observables such as the spatially averaged pressure. The same residual contribution reshapes the barrier geometry, ridge/valley structure, and interfacial anomalies of the fixed-global-temperature free-energy landscape. Numerical examples based on the van der Waals model illustrate the resulting landscape structure, and estimates of experimental scales suggest a setup for detecting the effective-gravity inversion.

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

3 major / 2 minor

Summary. The paper constructs a variational free-energy function for liquid-gas coexistence in heat-conducting fluids under weak gravity at fixed global temperature. It decomposes this free energy into a configurational part identical in form to the equilibrium weak-gravity free energy (with g replaced by an effective gravity g_eff) that controls the first-order configurational transition between separated liquid-gas arrangements, plus a residual excess-latent-heat contribution that vanishes without heat conduction. The residual term is required to recover the fundamental relation in laboratory variables and observables such as spatially averaged pressure; it also modifies the free-energy landscape. Numerical results from the van der Waals model illustrate the landscape, and experimental scales are estimated for detecting g_eff inversion.

Significance. If the asserted decomposition holds without additional assumptions, the work provides a systematic global-thermodynamic treatment of non-equilibrium phase coexistence under simultaneous gravity and heat flow, extending equilibrium weak-gravity results via an effective gravity while isolating the role of latent-heat transport. The separation into configuration-determining and observable-recovering parts, together with the van der Waals numerics and experimental estimates, offers a concrete route to testable predictions in steady-state thermodynamics.

major comments (3)
  1. [Abstract / §2–3] Abstract and the central construction (presumably §2–3): the decomposition of the fixed-global-temperature variational free energy into F_config(g_eff) + F_residual is asserted to be exact, with F_config identical in form to the known equilibrium functional and F_residual vanishing identically when the heat current is zero. No explicit derivation from the global-thermodynamic postulates or from the van der Waals equation of state is supplied; without this step the claim that F_config alone determines the first-order transition cannot be verified and remains the load-bearing assumption.
  2. [Abstract / §3] The definition and independence of the effective gravity g_eff: the manuscript introduces g_eff as the replacement that makes the configurational part match the equilibrium form, yet provides no independent determination (e.g., from local force balance or from the steady-state heat-current constraint) that would avoid circularity when locating the transition point.
  3. [§4] Recovery of laboratory observables: the claim that the residual term is required to obtain the fundamental relation in laboratory variables and the spatially averaged pressure is central, but the explicit mapping from the decomposed free energy to these quantities (including any integration over the interface or averaging procedure) is not shown in sufficient detail to confirm consistency with known limits (zero heat current, zero gravity).
minor comments (2)
  1. [Abstract] Notation for the residual excess-latent-heat contribution should be introduced with an explicit symbol and its functional dependence on the heat current stated at first use.
  2. [§5] The numerical examples would benefit from a brief statement of the discretization or minimization method used to obtain the landscape structure.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thorough reading and for identifying the points where additional detail would strengthen the manuscript. We address each major comment below and will incorporate the requested clarifications and derivations in a revised version.

read point-by-point responses

  1. Referee: [Abstract / §2–3] Abstract and the central construction (presumably §2–3): the decomposition of the fixed-global-temperature variational free energy into F_config(g_eff) + F_residual is asserted to be exact, with F_config identical in form to the known equilibrium functional and F_residual vanishing identically when the heat current is zero. No explicit derivation from the global-thermodynamic postulates or from the van der Waals equation of state is supplied; without this step the claim that F_config alone determines the first-order transition cannot be verified and remains the load-bearing assumption.

    Authors: We agree that the decomposition step requires an explicit derivation to be fully verifiable. In the revised manuscript we will add a dedicated subsection (new §2.3) that starts from the global-thermodynamic postulates, introduces the fixed-global-temperature variational functional, and carries out the decomposition algebraically, showing that the configurational term recovers the equilibrium weak-gravity form upon the replacement g → g_eff while the residual term is proportional to the heat current and vanishes identically when the current is zero. The same derivation will be repeated for the van der Waals equation of state to confirm that the transition location is indeed controlled solely by the configurational part. revision: yes

  2. Referee: [Abstract / §3] The definition and independence of the effective gravity g_eff: the manuscript introduces g_eff as the replacement that makes the configurational part match the equilibrium form, yet provides no independent determination (e.g., from local force balance or from the steady-state heat-current constraint) that would avoid circularity when locating the transition point.

    Authors: We will revise §3 to supply an independent expression for g_eff obtained directly from the steady-state force balance and the constraint of constant heat current, without reference to the location of the configurational transition. This expression will be derived from the local momentum and energy equations under the weak-gravity, steady-state assumptions and will be shown to reduce to the known equilibrium gravity when the heat current vanishes, thereby removing any appearance of circularity. revision: yes

  3. Referee: [§4] Recovery of laboratory observables: the claim that the residual term is required to obtain the fundamental relation in laboratory variables and the spatially averaged pressure is central, but the explicit mapping from the decomposed free energy to these quantities (including any integration over the interface or averaging procedure) is not shown in sufficient detail to confirm consistency with known limits (zero heat current, zero gravity).

    Authors: We accept that the mapping from the decomposed free energy to laboratory observables needs to be written out explicitly. In the revised §4 we will insert the intermediate steps that relate the total variational functional to the fundamental relation in laboratory variables, including the explicit surface integrals across the interface and the spatial averaging procedure for pressure. We will then verify that both the zero-heat-current and zero-gravity limits recover the standard equilibrium expressions, as required. revision: yes

Circularity Check

0 steps flagged

No significant circularity; construction of variational free energy is the core contribution

full rationale

The paper explicitly constructs the variational free-energy function for the fixed-global-temperature description and then decomposes it by definition into the configurational part (matching equilibrium form with g replaced by g_eff) plus residual term. This is presented as the modeling step rather than a derived claim that reduces to inputs by construction. Numerical illustrations use the independent van der Waals equation of state. No load-bearing self-citations, fitted inputs renamed as predictions, or uniqueness theorems imported from prior author work are indicated in the text. The framework is self-contained against external benchmarks such as the van der Waals model.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 2 invented entities

The central claim rests on the validity of the variational construction and the decomposition, which are postulated in the abstract without prior independent evidence mentioned.

axioms (2)
  • domain assumption The system can be described using a fixed-global-temperature variational principle.
    The paper constructs the free-energy for fixed-global-temperature description.
  • ad hoc to paper The free-energy decomposes into configurational and residual parts as described.
    The decomposition is central to the approach.
invented entities (2)
  • effective gravity no independent evidence
    purpose: To replace actual gravity in the configurational free energy to determine the transition.
    Introduced to account for heat conduction effects in the equilibrium-like part.
  • residual excess-latent-heat contribution no independent evidence
    purpose: To account for heat conduction effects needed for lab variables and observables.
    Vanishes without heat conduction, reshapes landscape.

pith-pipeline@v0.9.1-grok · 5695 in / 1554 out tokens · 46248 ms · 2026-06-28T20:09:57.681276+00:00 · methodology

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Reference graph

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