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pith:WG2AZZIR

pith:2026:WG2AZZIREO3QWHWM5BBJWD5UQD

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Theory of melting lines with a variable enthalpy of fusion

Anthony N. Papathanassiou

Accounting for variable enthalpy of fusion in the Clausius-Clapeyron equation yields approximate parabolic melting lines.

arxiv:2605.17631 v1 · 2026-05-17 · cond-mat.stat-mech

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Claims

C1strongest claim

Our derivation, rooted in solid-state anharmonicity, yields approximate parabolic scaling laws that corroborate with a recent universal model derived from the Phonon Theory of Liquids [K. Trachenko, Phys. Rev. E 109, 034122 (2024)], supporting the universal parabolic nature of melting curves from a completely distinct theoretical foundation.

C2weakest assumption

The isobaric heat capacity of crystalline solids near the melting point features a dominant anharmonic, volume-dependent component that directly correlates the latent heat to the specific volumes of the coexisting phases (abstract and methodology paragraph).

C3one line summary

Derives approximate parabolic melting-line equations from a modified Clausius-Clapeyron relation that incorporates volume-dependent latent heat arising from anharmonic contributions to the solid's isobaric heat capacity.

References

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[1] Differential equation of a ML First-order phase transitions are governed by the CC equation (Eq. (1). For a solid -liquid boundary, the slope 𝑑𝑃 𝑑𝑇𝑚 of the ML in a pressure -temperature (𝑃 − 𝑇) diagra

[2] (10) is: 𝑃(𝑇𝑚) ≅ 𝑑 𝑏 𝑇𝑚 − 𝑐1 𝑏 𝑒−𝑏𝑇𝑚 + 𝑐2 (13) where 𝑐1 and 𝑐2 are integration constants

[3] Approximate quadratic solution for small values of the term 𝒃𝑻𝒎 The Taylor expansion of the term 𝑒−𝑏𝑇𝑚 for small values of the positive quantity 𝑏𝑇𝑚 can be expressed as: 𝑒−𝑏𝑇𝑚 ≈ 1 − 𝑏𝑇𝑚 + 1 2 𝑏2𝑇𝑚 2 (

[4] (10) can be reduced to the following simple form: 𝑑2𝑃 𝑑𝑇𝑚2 ≅ 𝑑 > 0 (20) A general solution of the differential equation, Eq 1970

Receipt and verification

First computed	2026-05-20T00:04:49.545797Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b1b40ce51123b70b1ecce8429b0fb480d659e31de8b2400758f817de6c393fec

Aliases

arxiv: 2605.17631 · arxiv_version: 2605.17631v1 · doi: 10.48550/arxiv.2605.17631 · pith_short_12: WG2AZZIREO3Q · pith_short_16: WG2AZZIREO3QWHWM · pith_short_8: WG2AZZIR

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  | jq -c '.canonical_record' \
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Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "889d7beffc638babfd8c9576ea9ea6e81effd07475d1d8515c46230250b65b0f",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-17T19:52:07Z",
    "title_canon_sha256": "de7b53230127d9c6141168de5e3d3b8759c78056c235fb7ba5d1236897f01d71"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.17631",
    "kind": "arxiv",
    "version": 1
  }
}