Constitutive Settings with regard to Energy- and Entropy-Balances in Non-Equilibrium Thermodynamics: the Thermodynamical Verification

Wolfgang Muschik

REVIEW 1 major objections 2 minor 2 references

Internal settings connect energy and entropy balances due to flux interdependence in non-equilibrium thermodynamics

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2026-06-27 22:35 UTC pith:PQ3PDZCU

load-bearing objection The paper introduces 'thermodynamical verification' but asserts without derivation that interdependence of fluxes and differentials implies connection via 'internal settings'. the 1 major comments →

arxiv 2606.06131 v1 pith:PQ3PDZCU submitted 2026-06-04 physics.class-ph

Constitutive Settings with regard to Energy- and Entropy-Balances in Non-Equilibrium Thermodynamics: the Thermodynamical Verification

Wolfgang Muschik This is my paper

classification physics.class-ph

keywords non-equilibrium thermodynamicsconstitutive equationsenergy balanceentropy balancethermodynamical verificationinternal settings

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper introduces thermodynamical verification as a procedure to ensure constitutive equations agree with both energy- and entropy-balances. Heat flux and entropy flux, together with the time differentials of internal energy and entropy, are not independent of each other. This interdependence links the two balances through internal settings. The settings establish the theoretical frame of the material description and are supplemented by additional constitutive settings. A reader would care because the approach provides a way to maintain consistency between constitutive relations and the balance laws in thermodynamic modeling.

Core claim

Constitutive equations have to be in agreement with the energy- and entropy-balances. For achieving that, the procedure of thermodynamical verification is introduced: Because heat flux and entropy flux as well as the time differentials of internal energy and entropy are not independent of each other, energy- and entropy-balances are connected with each other by so-called internal settings laying down the theoretical frame of the applied material description which is characterized by additional constitutive settings.

What carries the argument

Internal settings that connect the energy- and entropy-balances by exploiting the interdependence of heat flux, entropy flux, and the time differentials of internal energy and entropy.

Load-bearing premise

The interdependence of heat flux, entropy flux, and the time differentials of internal energy and entropy requires internal settings to connect the balances.

What would settle it

An explicit construction of constitutive equations that satisfy both balances without any internal settings would show the connection is unnecessary.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Desk Editor's Note

The paper introduces 'thermodynamical verification' but asserts without derivation that interdependence of fluxes and differentials implies connection via 'internal settings'.

read the letter

The main point is that this paper introduces a procedure called thermodynamical verification to ensure constitutive equations respect both energy and entropy balances in non-equilibrium thermodynamics. It rests on the observation that heat flux, entropy flux, and the time rates of change of internal energy and entropy are interdependent, so the two balances are linked through what it calls internal settings that define the material description frame, plus further constitutive settings.

The paper does well to restate that these quantities are not independent, which is a basic fact in the field and worth keeping in view when writing down constitutive relations. That reminder is accurate and directly relevant to anyone setting up balance-consistent models.

The soft spots are in the execution. The step from non-independence to the existence and role of these internal settings is asserted rather than derived. There is no explicit relation shown to standard identities such as the local Gibbs relation or the entropy-production inequality, no definition of what counts as an internal setting, and no example that shows how the verification procedure actually constrains a constitutive equation in practice. Without those pieces the procedure stays at the level of a claim rather than a usable method, and it is impossible to judge whether it differs from existing consistency checks in the literature.

This is written for a narrow audience already working on the axiomatic side of non-equilibrium constitutive theory. Broader readers in applied thermo or modeling will not find operational guidance.

I would not send it to peer review in this form. The central inference does not stand on its own without the missing derivations and examples. If the full manuscript supplies those, the assessment could shift.

Referee Report

1 major / 2 minor

Summary. The manuscript introduces a 'thermodynamical verification' procedure to ensure constitutive equations agree with energy- and entropy-balances in non-equilibrium thermodynamics. It claims that the non-independence of heat flux, entropy flux, and the time differentials of internal energy and entropy connects the two balances through 'internal settings' that define the theoretical frame of the material description, which is further characterized by additional constitutive settings.

Significance. If the internal settings were explicitly defined, derived from standard balance laws or entropy-production inequalities, and illustrated with at least one concrete constitutive model, the procedure could provide a useful consistency check for material modeling. As presented, the claim restates a known interdependence without new derivations, examples, or operational content, limiting its potential impact.

major comments (1)

Abstract: the central inference that non-independence of the fluxes and time differentials 'directly' requires 'internal settings' to connect the balances is asserted without derivation, without reference to the local energy balance, entropy balance, or Gibbs relation, and without an example of how an internal setting is constructed or verified. This assertion is load-bearing for the entire proposed procedure.

minor comments (2)

The title is overly long and does not clearly indicate the absence of explicit derivations or examples.
No citations to standard references on constitutive theory (e.g., works on rational thermodynamics or extended irreversible thermodynamics) are provided to situate the 'internal settings' relative to existing approaches.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed reading of the manuscript. Below we address the single major comment point by point.

read point-by-point responses

Referee: Abstract: the central inference that non-independence of the fluxes and time differentials 'directly' requires 'internal settings' to connect the balances is asserted without derivation, without reference to the local energy balance, entropy balance, or Gibbs relation, and without an example of how an internal setting is constructed or verified. This assertion is load-bearing for the entire proposed procedure.

Authors: The abstract is deliberately concise. The body of the manuscript begins from the standard local statements of the energy balance and the entropy balance, notes the non-independence of the heat flux, entropy flux, and the material time derivatives of internal energy and entropy, and introduces the internal settings precisely as the relations that close this interdependence within a chosen material description. The Gibbs relation enters through the entropy balance in the usual way. The internal settings are therefore not an additional postulate but the explicit statement of the theoretical frame that makes the two balances consistent for any subsequent constitutive choices. We agree that an explicit worked example would strengthen the presentation and are prepared to add one in revision. revision: partial

Circularity Check

1 steps flagged

Internal settings introduced by definition to connect balances due to asserted non-independence of fluxes and differentials.

specific steps

self definitional [Abstract]
"Because heat flux and entropy flux as well as the time differentials of internal energy and entropy are not independent of each other, energy- and entropy-balances are connected with each other by so-called internal settings laying down the theoretical frame of the applied material description which is characterized by additional constitutive settings."

The sentence asserts non-independence as the cause for the existence of internal settings, yet the settings are introduced precisely to connect the balances and to characterize the material description via constitutive settings; the connection is therefore true by the definition of the settings rather than derived from prior independent relations.

full rationale

The abstract presents the non-independence of heat flux, entropy flux, dU/dt and dS/dt as the reason that balances are connected via internal settings, but those settings are defined exactly as the additional constitutive elements that lay down the material frame and enforce the connection. This makes the claimed link between non-independence and the verification procedure self-definitional rather than independently derived. No further equations or external benchmarks are supplied in the provided text to break the definitional loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only provides no explicit free parameters, axioms, or invented entities; the interdependence of fluxes and differentials is presented as a given without further breakdown.

pith-pipeline@v0.9.1-grok · 5599 in / 1022 out tokens · 19242 ms · 2026-06-27T22:35:12.247873+00:00 · methodology

0 comments

read the original abstract

Constitutive equations have to be in agreement with the energy- and entropy- balances. For achieving that, the procedure of thermodynamical verification is introduced: Because heat flux and entropy flux as well as the time differentials of internal energy and entropy are not independent of each other, energy- and entropy-balances are connected with each other by so-called internal settings laying down the theoretical frame of the applied material description which is characterized by additional constitutive settings.

discussion (0)

Reference graph

Works this paper leans on

2 extracted references · 1 canonical work pages

[1]

Papenfuß, C.:Continuum Thermodynamics and Constitutive Theory; Springer Nature: Switzerland, 2020; Chapter 3.3; doi.org/10.1007/978- 3-030-43989-7

work page doi:10.1007/978- 2020
[2]

Muschik, W.: Aspects of Non-Equilibrium Thermodynamics. Sect. 1.2. World Scientific, Singapore, 1990

1990

[1] [1]

Papenfuß, C.:Continuum Thermodynamics and Constitutive Theory; Springer Nature: Switzerland, 2020; Chapter 3.3; doi.org/10.1007/978- 3-030-43989-7

work page doi:10.1007/978- 2020

[2] [2]

Muschik, W.: Aspects of Non-Equilibrium Thermodynamics. Sect. 1.2. World Scientific, Singapore, 1990

1990