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arxiv: 1907.01811 · v1 · pith:JEGQJJ6Fnew · submitted 2019-07-03 · ❄️ cond-mat.other

Reply to comment on 'Surface thermodynamics and surface stress for deformable bodies'

Juan Olives (CINaM) This is my paper

Pith reviewed 2026-05-25 09:48 UTC · model grok-4.3

classification ❄️ cond-mat.other
keywords surface thermodynamicssurface stressdeformable bodiesEulerian descriptionLagrangian descriptiongrand potentialsurface energy variation
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0 comments X

The pith

The Eulerian forms of surface grand potential and energy variation are exactly equivalent to their Lagrangian counterparts.

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

The paper establishes the exact equivalence between Eulerian and Lagrangian expressions for the relation linking surface grand potential per unit area, surface stress, and surface strain. It also derives the variation of surface energy arising from both the deformation of an existing surface element and the creation of a new element. These results follow from an earlier introduction of the 'ideal transformation' method that fixes the local thermodynamic state variables of the surface. A sympathetic reader would care because surface quantities are defined via excesses rather than intuitive local values, so the equivalence removes a source of confusion in applying thermodynamics to any deformable body.

Core claim

By explicitly writing the Eulerian versions, the paper shows that the relation between the surface grand potential per unit area, the surface stress and the surface strain is identical to the Lagrangian form, and that the variation of the surface energy due to deformation of an element plus creation of a new element follows the same structure in both descriptions.

What carries the argument

The 'ideal transformation' that determines the local thermodynamic variables of the surface state and yields the exact work of surface deformation.

If this is right

  • The work of deformation of the surface receives an exact expression valid for any deformable body.
  • Surface stress receives a definition that holds independently of the choice of description (Eulerian or Lagrangian).
  • The distinction between deforming an existing surface element and creating a new one becomes unambiguous in both coordinate systems.

Where Pith is reading between the lines

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

  • The equivalence may allow existing Lagrangian codes in continuum surface mechanics to be re-used with Eulerian data without reformulation.
  • The same separation of deformation versus creation terms could be tested in growing interfaces such as crystal surfaces or biological membranes.

Load-bearing premise

An ideal transformation correctly fixes the local thermodynamic variables of the surface state without extra postulates on how surface excesses are defined.

What would settle it

A direct calculation or measurement in which the Eulerian and Lagrangian expressions for the surface grand potential relation yield numerically different values for the same physical surface would falsify the claimed exact equivalence.

read the original abstract

The above comment http://dx.doi.org/10.1088/0953-8984/22/42/428001 and a previous letter by the same author reveal a great misunderstanding of what Eulerian and Lagrangian quantities are, and a confusion between the deformation of an element of a surface and the creation of a new element of a surface. Surface thermodynamics is complex because the surface quantities are not 'intuitive' (as surface excesses on some dividing surface) and the thermodynamic variables of the state of a surface are a priori completely unknown. This is why we introduced a new concept ('ideal transformation') and presented detailed proof, leading to the determination of the 'local' thermodynamic variables of the state of the surface, the exact expression of the work of deformation of the surface, and the definition of surface stress, for any deformable body (Olives 2010 J. Phys.: Condens. Matter 22 085005, arXiv:arXiv:1906.11022). These results are not obvious (despite their similarity with some expressions in volume thermodynamics). We explicitly write the Eulerian forms of (i) the relation between the surface grand potential per unit area, the surface stress and the surface strain, showing its exact equivalence with the Lagrangian form, and (ii) the variation of the surface energy due to both the deformation of an element of the surface and the creation of a new element of the surface.

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

2 major / 2 minor

Summary. This manuscript is a reply to a comment on the authors' 2010 paper concerning surface thermodynamics and surface stress for deformable bodies. It argues that the comment (and a prior letter) misunderstands Eulerian versus Lagrangian quantities and confuses the deformation of an existing surface element with the creation of a new surface element. The authors assert that they explicitly write the Eulerian forms of (i) the relation between surface grand potential per unit area, surface stress, and surface strain (showing exact equivalence to the Lagrangian form) and (ii) the variation of surface energy due to both deformation and creation of surface elements, all derived from the 'ideal transformation' concept introduced in their prior work.

Significance. If the claimed exact equivalences hold and are clearly demonstrated, the reply could usefully clarify distinctions in surface thermodynamic formulations for deformable bodies and help resolve specific misunderstandings. Its significance is primarily clarificatory and tied to the 2010 framework rather than introducing independent results or external benchmarks.

major comments (2)
  1. The central claim of exact equivalence between Eulerian and Lagrangian forms rests entirely on re-expressing quantities defined via the 'ideal transformation' and local state variables from the 2010 paper (cited as Olives 2010 J. Phys.: Condens. Matter 22 085005); without the algebraic steps or an independent check visible, the equivalence reduces to an internal consistency within that self-contained framework rather than a new verification.
  2. The determination of local thermodynamic variables of the surface state is carried over from the 2010 definitions without additional justification or comparison to alternative approaches for defining surface excesses; this assumption is load-bearing for both claimed Eulerian expressions.
minor comments (2)
  1. The abstract states that the Eulerian forms are 'explicitly written' but does not display the expressions; including at least the key equations in the abstract or a summary table would improve accessibility for readers of the reply.
  2. The manuscript cites only the 2010 paper and the comment being answered; adding one or two references to independent treatments of Eulerian/Lagrangian surface thermodynamics would help situate the clarification.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and address the major comments point by point below.

read point-by-point responses

  1. Referee: The central claim of exact equivalence between Eulerian and Lagrangian forms rests entirely on re-expressing quantities defined via the 'ideal transformation' and local state variables from the 2010 paper (cited as Olives 2010 J. Phys.: Condens. Matter 22 085005); without the algebraic steps or an independent check visible, the equivalence reduces to an internal consistency within that self-contained framework rather than a new verification.

    Authors: The manuscript explicitly writes the Eulerian forms of (i) the relation between the surface grand potential per unit area, surface stress, and surface strain, and (ii) the variation of surface energy due to deformation and creation of surface elements, demonstrating their exact equivalence to the Lagrangian forms. These expressions follow directly from the ideal transformation concept, with the full algebraic derivations and proofs provided in the 2010 paper. The reply is intended to clarify the Eulerian-Lagrangian distinction for readers of the comment by presenting these equivalent expressions. revision: no

  2. Referee: The determination of local thermodynamic variables of the surface state is carried over from the 2010 definitions without additional justification or comparison to alternative approaches for defining surface excesses; this assumption is load-bearing for both claimed Eulerian expressions.

    Authors: The local thermodynamic variables of the surface state are determined in the 2010 paper through the ideal transformation and detailed proofs. As a targeted reply addressing specific misunderstandings in the comment regarding Eulerian versus Lagrangian quantities and surface element deformation versus creation, the manuscript does not repeat those derivations or compare to other surface excess definitions. The focus remains on the explicit Eulerian equivalents within the established framework. revision: no

Circularity Check

1 steps flagged

Equivalence claim reduces to re-expression of 2010 self-cited framework

specific steps
  1. self citation load bearing [Abstract]
    "we introduced a new concept ('ideal transformation') and presented detailed proof, leading to the determination of the 'local' thermodynamic variables of the state of the surface, the exact expression of the work of deformation of the surface, and the definition of surface stress, for any deformable body (Olives 2010 J. Phys.: Condens. Matter 22 085005, arXiv:arXiv:1906.11022). These results are not obvious (despite their similarity with some expressions in volume thermodynamics). We explicitly write the Eulerian forms of (i) the relation between the surface grand potential per unit area, the "

    The paper asserts it shows exact equivalence between Eulerian and Lagrangian forms of the grand-potential/stress/strain relation. However, the local thermodynamic variables, work expression, and surface stress are determined by the detailed proof in the self-cited 2010 paper by the same author. The equivalence therefore reduces to re-expressing quantities already fixed by that earlier framework rather than constituting an independent derivation.

full rationale

The reply's central content is the explicit writing of Eulerian forms for the grand-potential/stress/strain relation and energy variation, with asserted exact equivalence to Lagrangian versions. This equivalence and the underlying local state variables, work of deformation, and surface stress definitions are justified solely by reference to the author's own 2010 paper (same author, same concepts including 'ideal transformation'). No independent derivation or external benchmark is provided in the present text; the claimed results therefore reduce to re-expressing quantities fixed by the prior self-work. This constitutes self-citation load-bearing circularity for the core claim, though the paper performs the coordinate rewriting step itself.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim depends on the validity of the 'ideal transformation' concept introduced in the authors' prior work and on the premise that surface thermodynamic variables must be treated as a priori unknown rather than as simple excesses.

axioms (2)
  • domain assumption Surface quantities are not intuitive as surface excesses on some dividing surface
    Stated directly in the abstract as the reason a new concept was needed.
  • domain assumption The thermodynamic variables of the state of a surface are a priori completely unknown
    Invoked to justify introduction of the ideal-transformation concept.
invented entities (1)
  • ideal transformation no independent evidence
    purpose: To determine the local thermodynamic variables of the state of the surface and the exact expression for the work of deformation
    Introduced in the 2010 paper and relied upon here; no independent falsifiable handle is provided in the abstract.

pith-pipeline@v0.9.0 · 5784 in / 1464 out tokens · 38258 ms · 2026-05-25T09:48:19.395164+00:00 · methodology

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