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REVIEW 4 major objections 5 minor 300 references

The total energy approach for calculating the specific heat of liquids and glasses

T0 review · 4 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read The paper argues that the specific heat of liquids and glasses can be obtained directly from the total energy in adiabatic first-principles molecular dynamics, without phonon decompositions or empirical parameters, and that the resulting fr

desk verdict A clear but overclaiming review of the author's adiabatic total-energy method; the phonon critique has teeth, the universal/parameter-free claim does not. read the letter →

arxiv 2508.20630 v1 pith:YHPVE4LJ submitted 2025-08-28 cond-mat.dis-nn cond-mat.stat-mech

K. Shirai This is my paper · ORCID
classification cond-mat.dis-nncond-mat.stat-mech MSC 82B3082D30 PACS 65.20.-w64.70.Pc
keywords specificheatliquidsglassesfirst-principlesmoleculardynamicsdensityfunctionaltheoryglasstransitionatomrelaxationhysteresis
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This review argues that the specific heat of liquids and glasses should be computed by the total energy approach: take the internal energy U directly from density-functional-theory molecular dynamics, then differentiate with respect to temperature. It claims that liquids have no true eigenstates, so the additive quasi-particle decomposition that underlies phonon theory is not valid, and the real obstacle is atom relaxation rather than the absence of periodicity. The paper uses the second law of thermodynamics to justify assigning temperature from the time-averaged kinetic energy in adiabatic NVE simulations, and shows that this reproduces the falling heat capacity of liquid sodium and, for the first time without empirical parameters, the specific-heat jump at the glass transition of glycerol. If the argument is right, it gives a universal, parameter-free route to the heat capacities of disordered materials and recasts the glass transition as a thermodynamic transition rather than a nonequilibrium state.

What carries the argument

The load-bearing object is the pair formed by the total energy approach and the adiabatic relaxation simulation: direct time-averaging of the density-functional total energy in constant-NVE molecular dynamics, with temperature assigned through the equipartition relation (3/2)kBT = (1/2)⟨M v^2⟩ from the time-averaged kinetic energy. The thermodynamic justification is a modern statement of the second law asserting that for fixed internal energy and fixed constraints there is exactly one stable equilibrium state; this licenses the mapping from (U, initial atomic positions) to (T, equilibrium atomic positions). For solids, the internal energy separates into a structural part Est and a phonon par

What would settle it

Run two adiabatic NVE simulations of the same liquid with the same total energy and volume but very different initial atomic configurations, and wait until the structural relaxation completes. If the two runs settle at measurably different time-averaged temperatures, the uniqueness premise behind the method fails; if they converge to the same temperature, the central mapping survives.

Watch

Extended reading notes

Core claim

The central claim is that the isochoric specific heat of any material phase, including liquids and glasses, is obtained by computing U(T) as the time average of the DFT total energy over adiabatic (NVE) molecular dynamics and taking the numerical derivative. The paper contrasts this total energy approach with the elemental excitation approach, in which total energy is the sum of independent quasi-particle energies; that additive property holds only for eigenstates, and liquids lack eigenstates because atom relaxation destroys them. The author's calculations show that the structural energy term Est, which carries configurational and relaxation contributions, is responsible for the specific-he

Load-bearing premise

The load-bearing premise is that an isolated system with fixed total energy and fixed constraints has exactly one stable equilibrium state, and that a finite-size adiabatic molecular-dynamics run actually reaches it, so the time-averaged kinetic energy of the simulated atoms can be read as the thermodynamic temperature.

Editorial extensions

If this is right

  • For any material whose DFT forces are affordable, CV and, by integration, CP and free energies become computable with no empirical input, including for supercooled liquids and glasses.
  • The glass transition is classified as a structural, thermodynamically driven transition: below Tg the glass, not the liquid, is the stable equilibrium state.
  • Observed hysteresis in C-T curves is compatible with equilibrium thermodynamics once equilibrium atomic positions are counted as state variables; history dependence no longer forces a nonequilibrium label.
  • Phonon-based estimates of liquid heat capacities may capture qualitative trends but cannot be the foundation of the theory, because the Bose-Einstein occupation of liquid phonons is not justified.
  • Finite-size rounding of melting converts part of latent heat into apparent specific heat, so sharp lambda-like peaks in disordered or small systems should be interpreted cautiously.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural next test is to apply the same adiabatic NVE protocol to molecular liquids with internal vibrational modes, especially water, whose large CP is unexplained by phonons; the sensitivity of the structural-energy term to long-range DFT functionals will likely decide whether the approach captures it.
  • Since the paper finds that the activation energy extracted from CV is much smaller than those from diffusion or viscosity, Arrhenius analysis of heat capacity could become a cheap experimental probe of the weakest relaxation channel in a liquid.
  • The finite-size argument suggests that broadened specific-heat peaks near transitions with disorder may contain a latent-heat component; comparing the integrated peak area with directly measured latent heat in a material such as quartz would test this interpretation.
  • If the glass transition is truly thermodynamic, the Prigogine-Defay ratio inequality should follow from the structural-energy change alone; the paper asserts this connection, and a numerical survey across many glass formers would strengthen it.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes a 'total energy approach' to computing the specific heat of liquids and glasses from first-principles molecular dynamics. Instead of decomposing the energy into phonon-like elemental excitations, the method uses direct adiabatic (NVE) DFT-MD simulations: for a fixed total energy U and initial atomic positions, the system is allowed to relax to an equilibrium state characterized by a temperature from the kinetic-energy average (Eq. 62). The GB statement of the second law is invoked to guarantee one stable equilibrium per (U, constraints), which makes the mapping (U,{R_j(0)})→(T,{R_j^K}) single-valued. The paper reviews experimental facts on C_V of liquids, emphasizes the role of atom relaxation and hysteresis, and presents two applications: the decreasing C_V(T) of liquid Na and the specific-heat jump ΔC_gl at the glass transition of glycerol. For glycerol, linear fits of the structural energy Est above and below T_g give ΔC_st = 0.58R; adding an estimated ΔC_te ≤ 0.15R yields ΔC_gl = 0.73R, compared with the experimental 0.70R. The calculated T_m and T_g for glycerol are 635 K and 310 K, versus experimental values of 291 K and 185 K.

Significance. If the central claim held, the method would be a significant conceptual advance: a parameter-free, theory-agnostic route to the specific heat of non-periodic systems, avoiding the questionable phonon decomposition for liquids. The paper gives proper credit to prior phonon-based work and clearly identifies the finite-size rounding of first-order transitions and the multi-timescale nature of relaxation as key physical issues. The honest reporting of the overestimated T_m and T_g and of the negative-slope artifact in the Si melting curves is a strength, as is the explicit discussion of hysteresis as a state-space projection effect. However, the quantitative centerpiece—the parameter-free ΔC_gl—depends on linear fits to scattered data and an order-of-magnitude estimate, and the conceptual cornerstone (uniqueness of the equilibrium state reached by finite-time NVE MD) is asserted rather than verified. The paper is therefore a thought-provoking review with suggestive results, but the universal, parameter-free claim is not yet established to the standards implied by the abstract.

major comments (4)
  1. [§4.3, Fig. 14] The central claim 'first time to calculate the jump ΔC_gl without any empirical parameter' is not supported with error analysis. The Est data are visibly scattered; ΔC_st = 0.58R comes from linear fits above and below T_g with no reported fit statistics, no error bars, and no sensitivity to the chosen T ranges. ΔC_te is 'estimated to be at most 0.15R', not calculated. The final ΔC_gl = 0.73R is thus a sum of an unquantified slope difference and an estimate. Without propagation of uncertainty, the agreement with the experimental 0.70R is suggestive but not demonstrated. The fact that T_g and T_m are overestimated by nearly a factor of two (310 K vs 185 K; 635 K vs 291 K) further leaves open the possibility that the agreement in ΔC_gl is coincidental.
  2. [§1.2 and §3.3.3, Eq. (60), Eq. (63)] The load-bearing premise is the GB uniqueness statement and the one-way mapping (U,{R_j(0)})→(T,{R_j^K}). The equilibrium checks in Eq. (63)—constant MSD for solids, linear MSD for liquids—only certify apparent stationarity on the simulation window. For a glass where structural relaxation times vastly exceed MD times, the check cannot distinguish a metastable basin from the unique stable equilibrium. The paper itself states that 'a large hysteresis indeed occurs' in Fig. 14 for cooling vs reheating, which demonstrates that different initial configurations at similar U reach different states. If the mapping is not single-valued on practical timescales, then U(T) is history-dependent and C = dU/dT is not a state function. A concrete test would be: for fixed U, start NVE runs from several independent configurations and show that the same T and the same {R_j^K} are reached within statistical
  3. [§4.1.1, Fig. 10] The liquid-sodium result, while qualitatively correct, is quantitatively off by about a factor of two: the computed dC_V/dT = −0.94×10^-3 R/K versus the experimental −1.6×10^-3 R/K, with the origin of the discrepancy left 'unclear'. Moreover, the region 370 < T < 500 K is handled by a linear interpolation of U(T), producing a constant C_V = 4.05R that the authors explicitly say 'does not have physical meaning and should not be compared with experiment'. Thus the universal, parameter-free prediction currently has predictive power only for the sign and rough magnitude of the temperature slope, not for the detailed shape of C_V(T) including the near-T_m region. This should be stated more prominently when the 'first time to demonstrate' claim is made for the decreasing behavior.
  4. [§3.3.3 and §4.2, Eq. (69), Fig. 13] Convergence with respect to system size is not demonstrated for the glass calculation. For Si, the finite-size width W_m remains about 300 K even for N=512 atoms, and Eq. (69) shows slow convergence as N^-1/2. The glycerol calculation does not state the cell size, the MD duration, or how many independent runs were used, although the Est data in Fig. 14 are 'scattered'. Because the linear fits used for ΔC_st are performed over a temperature range that includes finite-size rounding effects, a convergence study with N (e.g., 64, 216, 512 atoms) and a reporting of simulation lengths are necessary to establish that the obtained slope difference is not a finite-size artifact.
minor comments (5)
  1. [Throughout] Numerous typographical issues remain: 'a ffects', 'di fficult', 'Eherenfest' (should be Ehrenfest), 'di fference', 'visco se', 'overbinding of the LDA/GGA functional' is discussed without reference to the functional used in the glycerol calculations. A careful proofread is needed.
  2. [§3.3.3, Eq. (62)] The notation for the average in Eq. (62) is confusing: the brackets denote particle average and the bar denotes time average, but the expression ⟨M_j v_j(t)^2⟩_j mixes a particle index with a time argument. Clarify the order of averaging and the exact window used for the time average.
  3. [§4.3] The estimate ΔC_te ≤ 0.15R is stated without a derivation or a reference to a specific experimental value for glycerol's thermal expansion or compressibility near T_g. Since this term is added to obtain the headline number 0.73R, a one-source estimate is too thin; provide the underlying data or otherwise remove the term from the headline claim.
  4. [§5.3.3, Eq. (77)] The inequality G(gl) < G(li) for T < T_g is claimed to follow from d^2G/dT^2 = −C_P/T < 0. This is correct only if the liquid and glass curves are compared at the same T and if both are equilibrium branches; the derivation should explicitly state that the glass branch is treated as an equilibrium branch on the timescale of Eq. (41).
  5. [References] Several key claims rely on the author's own arXiv preprints (Refs. [35], [56], [259]) that are not peer-reviewed or not yet published. When these are load-bearing (e.g., the definition of state variables for solids and the detailed hysteresis treatment), the reader should be told which results are established in the current paper and which are taken from those preprints.

Circularity Check

0 steps flagged · score 1.0 of 10

No circular reduction identified; central ΔCgl is a direct DFT-MD slope, externally compared to experiment, though the review leans heavily on the author's own prior framework.

full rationale

The paper's numerical claims are obtained by differentiating the time-averaged internal energy U(T) of adiabatic (NVE) DFT-MD runs (Eqs. 24–25, 62), not by fitting experimental targets. The reported ΔCgl=0.73R is the difference of linear slopes of Est(T) above and below Tg (Sec. 4.3b), and the comparison with the experimental 0.70R is an external falsifiable benchmark. The GB uniqueness statement (Secs. 1.2 and 3.3.3) is an external axiom; its application to finite-time MD is a validity/correctness concern (finite-size effects, hysteresis, and Eq. 63 criteria certifying only apparent stationarity) but not a circular reduction. Self-citations are numerous ([32], [35], [50], [51], [52], [56], [180]) and support the conceptual apparatus, but the key predictions do not reduce to those citations: they were produced by earlier first-principles simulations and are checked against independent experimental data. No equation in the paper is defined in terms of the quantity it is claimed to predict. The score reflects the density of self-citation and the framework's reliance on the author's own definitions of state variables, not an identified circular derivation.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The framework relies on the GB axiom, the Born-Oppenheimer approximation, and the equipartition-based temperature definition, plus the multi-timescale separation that allows atomic positions to serve as state variables. No new physical particles or forces are introduced. The central numerical results are inherited from prior papers by the same author.

assumptions (5)
  • domain assumption GB statement of the second law: for fixed U and constraints, an isolated system has one and only one stable equilibrium state.
    Invoked in Section 1.2 and 3.3.3 to justify that adiabatic MD reaches the true equilibrium; this is an axiom of the framework, not derived.
  • standard math Born-Oppenheimer approximation separates electronic and ionic motion; DFT ground-state energy serves as the ion potential.
    Used throughout, e.g., Eq. (24), to express total energy as sum of kinetic and potential terms.
  • domain assumption The thermodynamic temperature is obtained from the time-averaged kinetic energy via the equipartition relation 3/2 kBT = 1/2 <M_j v_j^2> (Eq. 62).
    This is the basis for assigning T in adiabatic MD runs; it assumes classical thermalization.
  • domain assumption The hierarchy of relaxation times (Eq. 41) defines local equilibrium and allows assignment of state variables {R_j} to solid/glass states.
    Used to treat glass as an equilibrium state specified by atomic positions.
  • domain assumption The positive definiteness of CP and the relation d^2G/dT^2 = -CP/T imply G(gl)<G(li) for T<Tg (Section 5.3.3).
    Used to argue glass is thermodynamically stable; this inference depends on the temperature dependence of CP and the extrapolation of liquid properties.

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Pith. "Pith review of The total energy approach for calculating the specific heat of liquids and glasses." pith.science (2026). https://pith.science/paper/YHPVE4LJ

@misc{pith2026250820630,
  author       = {Pith},
  title        = {Pith review of: The total energy approach for calculating the specific heat of liquids and glasses},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YHPVE4LJ}},
  note         = {Machine review of arXiv:2508.20630}
}
abstract

The recent development of the calculation of specific heat ($C$) of liquids and glasses by first-principles molecular dynamics (MD) simulations is reviewed. Liquid and glass states have common properties in that there is no periodicity and the atom relaxation has an important role in their thermodynamic properties. These properties have, for a long time, hindered the construction of an appropriate theory of $C$ for these states. The total energy approach based on the density-functional theory (DFT) provides a universal method to calculate $C$, irrespective of the material states. However, aside from the convergence problem, even DFT-based MD simulations give different values for a thermodynamic property of liquids and glasses, depending on the setup of MD simulations. The essential problem is atom relaxation, which affects the relationship between the energy and temperature $T$. The temperature is determined by the equilibrium state, but there are many metastable states for glasses. Metastable states are stable within their relaxation times. We encounter the difficult problem of hysteresis, which is the most profound consequence of irreversibility. Irreversibility occurs even for quasistatic processes. This is the most difficult and confusing point in the thermodynamics literature. Here, a consistent treatment of both equilibrium properties and irreversibility in adiabatic MD simulations, which has no frictional term, is given by taking multi-timescales into account. A leading principle to determine the equilibrium is provided by the second law of thermodynamics. The basic ideas and the usefulness of the total energy approach in real calculations are presented.

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.