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arxiv: 2604.26302 · v1 · submitted 2026-04-29 · ❄️ cond-mat.soft · q-bio.QM

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A Thermodynamic Analysis of Enhanced Metastability in Isochoric Supercooled Liquids

Boris Rubinsky
Authors on Pith no claims yet

Pith reviewed 2026-05-07 12:56 UTC · model grok-4.3

classification ❄️ cond-mat.soft q-bio.QM
keywords thermodynamicssupercoolingnucleationmetastabilityisochoricHelmholtz free energyGibbs free energy
0
0 comments X

The pith

Constant-volume conditions weaken the thermodynamic driving force for solidification relative to constant-pressure conditions whenever the solid phase is less dense than the liquid.

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

The paper proves that the Helmholtz free energy change driving solidification is smaller under constant volume than the Gibbs free energy change under constant pressure for substances that expand upon freezing. This inequality is derived using equilibrium thermodynamics and a first-order perturbation to account for the volume constraint. Because crystal nucleation rates scale exponentially with the inverse square of the driving force, the reduced force under isochoric conditions suppresses nucleation and thereby enhances the stability of the supercooled liquid state. The analysis also introduces a dimensionless isochoric stability number that depends only on measurable bulk properties.

Core claim

For any substance undergoing phase transformation in which the solid is less dense than the liquid, the Helmholtz driving force for solidification in isochoric systems is smaller than the Gibbs driving force in isobaric systems. This provides a thermodynamic basis for the observed suppression of nucleation rates under volumetric constraint.

What carries the argument

The inequality between the isochoric Helmholtz driving force and the isobaric Gibbs driving force, obtained through first-order perturbation of the equilibrium free energy.

Load-bearing premise

The first-order perturbation accurately captures how the volume constraint modifies the free-energy driving force, and nucleation rates depend exponentially on the inverse square of that force.

What would settle it

A measurement showing that the Helmholtz driving force equals or exceeds the Gibbs driving force for a material where the solid is less dense than the liquid would disprove the central inequality.

Figures

Figures reproduced from arXiv: 2604.26302 by Boris Rubinsky.

Figure 1
Figure 1. Figure 1: Thermodynamic basis of isochoric freezing. (A) Pressure–temperature phase diagram showing the isochoric process path along the water–ice Ih liquidus to −21.9°C, 209.9 MPa at the triple point. The negative Clapeyron slope view at source ↗
Figure 2
Figure 2. Figure 2: Helmholtz free energy T–V phase diagram of water. (A) Free energy surfaces of liquid water and ice Ih as functions of temperature and specific volume; the common tangent construction (Lines of Dissipated Energy) gives the equilibrium pressure. (B) Projected T–V phase diagram with broad two-phase equilibrium region traversed by pressure isoclines. Nucleation in an isochoric system traces a vertical path; th… view at source ↗
read the original abstract

Experiments show that isochoric (constant-volume) conditions enhance supercooling stability relative to isobaric (constant-pressure) conditions. Here, combining Helmholtz equilibrium thermodynamics with a first-order perturbation methodology, we derive an inequality governing nucleation stability under volumetric constraint. The derivation provides a general thermodynamic proof that for any substance undergoing phase transformation in which the solid is less dense than the liquid, the Helmholtz driving force for solidification in isochoric systems is smaller than the Gibbs driving force in isobaric systems. Since nucleation rates depend exponentially on the inverse square of the driving force, this provides a thermodynamic basis for the observed suppression of nucleation rates. While a full stochastic treatment is beyond the scope of this work, the reduction in driving force implies a weakening of the bias toward growth of pre-critical fluctuations, increasing their probability of thermal dissolution. The analysis yields a dimensionless isochoric stability number. This number is computable from bulk thermodynamic data alone and provides a geometry-independent criterion for comparing metastable liquid stability across materials and conditions.

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. The paper claims that for any substance where the solid is less dense than the liquid, the Helmholtz driving force for solidification under isochoric conditions is smaller than the Gibbs driving force under isobaric conditions. This follows from equilibrium thermodynamics combined with a first-order perturbation treatment of the volumetric constraint, yielding a dimensionless isochoric stability number computable from bulk thermodynamic data. The reduced driving force is argued to suppress nucleation rates (via the exponential dependence on the inverse square of the driving force) and thereby enhance metastability in supercooled liquids.

Significance. If the central inequality holds beyond the perturbative regime, the work supplies a parameter-free thermodynamic explanation for experimentally observed isochoric stabilization of supercooled liquids and a practical, geometry-independent metric for comparing metastable stability across materials. The derivation from standard potentials and the explicit link to nucleation-rate scaling are strengths that could be tested against existing isochoric vs. isobaric data.

major comments (2)
  1. [§3, Eq. (8)] §3, Eq. (8) and the subsequent first-order expansion: the inequality ΔF_H < ΔG_G is obtained only at linear order in the volume perturbation ΔV; no remainder estimate or bound on quadratic (compressibility) or higher-order terms is supplied, leaving the claim of generality for arbitrary density contrasts or near-critical conditions unproven.
  2. [§4] §4, paragraph following Eq. (12): the assertion that the result applies to 'any substance' rests on the unverified assumption that the first-order term dominates; a counter-example or explicit condition on the magnitude of ΔV/V or the equation of state would be needed to support the scope.
minor comments (2)
  1. [§4] The definition of the isochoric stability number (introduced after Eq. (15)) should be stated explicitly as a single equation rather than described in prose, to facilitate direct computation from tabulated data.
  2. Notation: the symbols ΔF_H and ΔG_G are introduced without a dedicated nomenclature table; a brief list of thermodynamic potentials and their driving-force definitions would improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The comments correctly identify that our derivation of the inequality relies on a first-order perturbative expansion, and we agree that the manuscript should clarify the regime of validity rather than assert unrestricted generality. We address each major comment below and will revise the text accordingly.

read point-by-point responses

  1. Referee: [§3, Eq. (8)] §3, Eq. (8) and the subsequent first-order expansion: the inequality ΔF_H < ΔG_G is obtained only at linear order in the volume perturbation ΔV; no remainder estimate or bound on quadratic (compressibility) or higher-order terms is supplied, leaving the claim of generality for arbitrary density contrasts or near-critical conditions unproven.

    Authors: We agree that the inequality is derived at linear order in ΔV and that no explicit remainder bound is provided. The leading term yields ΔF_H < ΔG_G whenever the solid is less dense than the liquid. In the revised manuscript we will insert a short error analysis after Eq. (8) that estimates the quadratic correction using the isothermal compressibilities of the two phases; for the density contrasts typical of most materials (ΔV/V ≈ 0.05–0.15) the relative size of the quadratic term remains below a few percent except near critical points where compressibility diverges. We will also state explicitly that the result is perturbative and does not claim validity for arbitrarily large density contrasts. revision: yes

  2. Referee: [§4] §4, paragraph following Eq. (12): the assertion that the result applies to 'any substance' rests on the unverified assumption that the first-order term dominates; a counter-example or explicit condition on the magnitude of ΔV/V or the equation of state would be needed to support the scope.

    Authors: The phrase 'any substance' in the current text is imprecise. The derivation assumes that the volume change upon freezing is a small perturbation relative to the system volume and that the equation of state remains regular. In revision we will replace the unqualified statement with 'any substance whose solid phase is less dense than the liquid and whose density contrast satisfies ΔV/V ≪ 1 away from critical points.' We will add a brief paragraph noting that a counter-example would require either an extremely large density jump or proximity to a critical point where higher-order compressibility terms become dominant; such cases lie outside the intended scope of the first-order analysis. revision: yes

Circularity Check

0 steps flagged

No circularity; central inequality follows from standard thermodynamics plus first-order perturbation without reduction to inputs

full rationale

The paper's derivation begins from equilibrium Helmholtz thermodynamics and applies a first-order perturbative expansion to the volumetric constraint. The resulting inequality for the driving force difference is obtained directly from the sign of the density contrast (solid less dense than liquid) at linear order in ΔV. No step renames a fitted quantity as a prediction, invokes a self-citation as the sole justification for a uniqueness claim, or defines the target result in terms of itself. The analysis remains self-contained against external thermodynamic benchmarks and does not rely on any load-bearing self-referential construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard thermodynamic identities and a perturbation approximation; no free parameters are introduced and no new physical entities are postulated.

axioms (2)
  • standard math Equilibrium relations between Helmholtz free energy (constant volume) and Gibbs free energy (constant pressure) for phase transformations
    Used as the starting point to compare driving forces under the two constraints.
  • domain assumption Validity of first-order perturbation methodology for incorporating the volumetric constraint into the free-energy difference
    Invoked to obtain the inequality governing nucleation stability.

pith-pipeline@v0.9.0 · 5473 in / 1363 out tokens · 77548 ms · 2026-05-07T12:56:54.073720+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

29 extracted references · 1 canonical work pages

  1. [1]

    Arbănaşi, T

    E.-M. Arbănaşi, T. V . Chirilă, Preservation of human vascular tissue and the relevance of temperature: a narrative review, Front. Bioeng. Biotechnol. 13 (2026)

    2026

  2. [2]

    Berendsen, B.G

    T.A. Berendsen, B.G. Bruinsma, C.F. Puts, N. Saeidi, O.B. Usta, B.E. Uygun, M.L. Izamis, M. Toner, M.L. Yarmush, K. Uygun, Supercooling enables long-term transplantation survival following 4 days of liver preservation, Nat. Med. 20 (2014) 790– 793

    2014

  3. [3]

    Berkane, J

    Y . Berkane, J. Hayau, I. Filz von Reiterdank, A. Kharga, L. Charlès, A.B. Mink van der Molen, J.H. Coert, N. Bertheuil, M.A. Randolph, C.L. Cetrulo, A. Longchamp, A.G. Lellouch, K. Uygun, Supercooling: a promising technique for prolonged preservation in solid organ transplantation, and early perspectives in vascularized composite allografts, Frontiers in...

    2023

  4. [4]

    Bilbao-Sainz, B.-S

    C. Bilbao-Sainz, B.-S. Chiou, G. Takeoka, T. Williams, D. Wood, M. Powell-Palm, B. Rubinsky, T. McHugh, Isochoric freezing and isochoric supercooling as innovative postharvest technologies for pomegranate preservation, Postharvest Biol. Technol. 194 (2022) 112072

    2022

  5. [5]

    Bilbao-Sainz, B

    C. Bilbao-Sainz, B. Rubinsky, Combined isochoric processes of freezing and supercooling., Npj Sci Food 9 (2025) 184

    2025

  6. [6]

    Botea, G

    F. Botea, G. Nastase, V . Herlea, T.T. Chang, A. Serban, A. Barcu, B. Rubinsky, I. Popescu, An exploratory study on isochoric supercooling preservation of the pig liver, Biochem. Biophys. Rep. 34 (2023) 1010485

    2023

  7. [7]

    Campean, G.A

    S.I. Campean, G.A. Beschea, A. Serban, I. Popescu, F. Botea, B. Rubinsky, G. NASTASE, Liquid-Solid Equilibria and Supercooling of Custodiol® in Isochoric and Isobaric Thermodynamic Systems at Subfreezing Temperatures, Available at SSRN 4432713 (n.d.)

  8. [8]

    Campean, G.-A

    S.-I. Campean, G.-A. Beschea, A. Serban, M.J. Powell-Palm, B. Rubinsky, G. Nastase, Analysis of the relative supercooling enhancement of two emerging supercooling techniques, AIP Adv. 11 (2021) 055125

    2021

  9. [9]

    Consiglio, D

    A.N. Consiglio, D. Lilley, R. Prasher, B. Rubinsky, M.J. Powell-Palm, Methods to stabilize aqueous supercooling identified by use of an isochoric nucleation detection (INDe) device, Cryobiology 106 (2022) 91–101

    2022

  10. [10]

    Consiglio, Y

    A.N. Consiglio, Y . Ouyang, M.J. Powell-Palm, B. Rubinsky, An extreme value statistics model of heterogeneous ice nucleation for quantifying the stability of supercooled aqueous systems, J. Chem. Phys 159 (2023) 064511

    2023

  11. [11]

    Huang, M.L

    H. Huang, M.L. Yarmush, O.B. Usta, Long-term deep-supercooling of large-volume water and red cell suspensions via surface sealing with immiscible liquids, Nat. Commun. 9 (2018) 3201

    2018

  12. [12]

    Jeong, S.-H

    C.-H. Jeong, S.-H. Lee, H.-Y . Kim, Optimization of dry-aging conditions for chicken meat using the electric field supercooling system, J. Anim. Sci. Technol. 66 (2024) 603–613

    2024

  13. [13]

    T. Kang, Y . You, S. Jun, Supercooling preservation technology in food and biological samples: a review focused on electric and magnetic field applications, Food Sci. Biotechnol. 29 (2020) 303–321

    2020

  14. [14]

    H. Kim, J. Lee, Y . Hur, C. Lee, S.-H. Park, B.-W. Koo, Marine Antifreeze Proteins: Structure, Function, and Application to Cryopreservation as a Potential Cryoprotectant, Mar. Drugs 15 (2017) 27

    2017

  15. [15]

    H. Lin, Y . Xu, W. Guan, S. Zhao, X. Li, C. Zhang, C. Blecker, J. Liu, The importance of supercooled stability for food during supercooling preservation: a review of mechanisms, influencing factors, and control methods, Crit. Rev. Food Sci. Nutr. 64 (2024) 12207– 12221

    2024

  16. [16]

    Năstase, F

    G. Năstase, F. Botea, G.-A. Beșchea, Ștefan-I. Câmpean, A. Barcu, I. Neacșu, V . Herlea, I. Popescu, T.T. Chang, B. Rubinsky, Isochoric Supercooling Organ Preservation System, Bioengineering 10 (2023) 934

    2023

  17. [17]

    M. Powell-Palm, Theoretical and Experimental Advances in the Development of Isochoric Cryopreservation Techniques https://escholarship.org/uc/item/92k2s6r9 , Ph.D., University of California Berkeley, 2020

    2020

  18. [18]

    Powell-Palm, V

    M.J. Powell-Palm, V . Charwat, B. Charrez, B. Siemons, K.E. Healy, B. Rubinsky, Isochoric supercooled preservation and revival of human cardiac microtissues, Commun. Biol. 4 (2021) 1118(2021)

    2021

  19. [19]

    Powell-Palm, A

    M.J. Powell-Palm, A. Koh-Bell, B. Rubinsky, Isochoric conditions enhance stability of metastable supercooled water, Appl.Phys.Lett 123702 (2020) https://doi.org/10.1063/1.5145334

    work page doi:10.1063/1.5145334 2020

  20. [20]

    Powell-Palm, B

    M.J. Powell-Palm, B. Rubinsky, W. Sun, Freezing water at constant volume and under confinement, Communications Physics (Nature) 3 (2020)

    2020

  21. [21]

    M. Puts, CF; Berendsen, TA; Uygun, K; Bruinsma, BG; Ozer, Sinan; Luitje, Martha; Usta, O Berk; Yarmush, Polyethylene glycol protects primary hepatocytes during supercooling preservation, Cryobiology 71 (2015) 125–129

    2015

  22. [22]

    Q. Ran, J. Zhang, J. Zhong, J. Lin, S. Zhang, G. Li, B. You, Organ preservation: current limitations and optimization approaches, Front. Med. (Lausanne). 12 (2025)

    2025

  23. [23]

    Reyna, JM

    J. Reyna, JM. Herrera, WJ. Chen, MT. Seyki, Y . Weng, ML. Dicke, AN. Consiglio, A. Maida, B. Rubinsky, TT. Chang, Tissue Orb: An Autonomous Perfused Bioreactor for the Generation and Cryopreservation of Vascularized Bioengineered Liver Tissues, in: Summer Liver Academy Meeting, 2024: p. June 16-20; Cape Coral, FL

    2024

  24. [24]

    Reyna, JM

    JC. Reyna, JM. Herrera, WJ. Chen, MT. Seyk, Y . Weng, ML. Dicker, AN. Consiglio, A. Maida, B. Rubinsky, TT. Chang, A Tissue Culture Platform for Vascularized Liver Tissue Generation and Cryopreservation in Low Earth Orbit., in: International Space Station Research & Development Conference;, 2024: p. July 30-August 1; Boston, MA

    2024

  25. [25]

    Rubinsky, P.A

    B. Rubinsky, P.A. Perez, E.M. Carlson, The thermodynamic principles of isochoric cryopreservation, Cryobiology 50 (2005) 121–138

    2005

  26. [26]

    Sheps, A.N

    N. Sheps, A.N. Consiglio, Y . Ouyang, T.T. Chang, B. Rubinsky, The effect of vibration and acceleration on the stability of isochoric (constant volume) supercooled aqueous systems, Med. Eng. Phys. 147 (2026) 015013

    2026

  27. [27]

    S. Teng, J. Li, H. Liu, K. Ye, Static magnetic field combined with phased cooling could maintain the supercooling state to improve the quality of pork during −4 °C storage, Food Chem. 506 (2026) 148116

    2026

  28. [28]

    O.B. Usta, Y . Kim, S. Ozer, BB. Bruinsma, J. Lee, E. Demir, C.F. Berendsenm T.A. Puts, M.-L. Izamis, K. Uygun, B.E. Uygun, M.L. Yarmush, Supercooling as a viable non- freezing cell preservaion method of rat hepatocytes, PLoS One 8 (2013) e69334

    2013

  29. [29]

    Wilson, J.P

    P.W. Wilson, J.P. Leader, Stabilization of supercooled fluids by thermal hysteresis proteins, Biophys. J. 68 (1995) 2098–2107

    1995