Pith. sign in

REVIEW 2 major objections 4 minor 82 references

Stochastic order parameter dynamics for phase coexistence in heat conduction

T0 review · 2 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A stochastic order-parameter model for phase coexistence in steady heat conduction predicts that the interface temperature deviates from the equilibrium transition temperature by a term proportional to the heat flux and the difference of…

desk verdict A serious paper with a new variational principle; the interface-temperature formula is the valuable conjecture, but the coefficient 1/3 rests on an admittedly phenomenological step, so treat (VI.40) as conditional until the interface contribution is derived. read the letter →

arxiv 1908.03029 v3 pith:7W3EIUUW submitted 2019-08-08 cond-mat.stat-mech

Shin-ichi Sasa , Naoko Nakagawa , Masato Itami , Yohei Nakayama This is my paper · ORCID
classification cond-mat.stat-mech MSC 82B2680A1982C3182C35 PACS 05.70.-a05.70.Ln05.40.-a
keywords stochasticthermodynamicsphasecoexistenceheatconductionorderparameterdynamicsvariationalprincipleinterfacetemperatureZubarev-McLennandistributionsuperheatedorderedstate
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 paper tries to establish that when two phases of a material coexist while heat steadily flows through them, the temperature of the interface between the phases is not the equilibrium transition temperature $T_c$. From a stochastic order parameter model of an order\u2013disorder transition with a flux-controlled boundary condition that conserves total energy, the authors derive a variational principle for the non-equilibrium steady state. Solving it gives $\theta^* - T_c = -(J/3)(1/\kappa_o - 1/\kappa_d)X_{eq}(1-X_{eq})$ to linear order in the heat flux $J$: the interface is hotter than $T_c$, with a superheated ordered state nearby, when the ordered phase conducts heat worse than the disordered phase, and colder, with a supercooled disordered state, in the opposite case. The result matters because it turns an earlier thermodynamic prediction into a concrete, testable statement about a stochastic microscopic model, and it shows that deterministic interface thermodynamics misses the effect entirely.

What carries the argument

The central object is a stochastic extension of phase-field dynamics: fields $m$ (order parameter), $v$ (its momentum), and $\varphi$ (energy density), with an entropy functional $S=\int (s(u,m) - (d_s/2)|\nabla m|^2)$ and noise obeying local detailed balance; the small parameter $\eta$, the ratio of microscopic to system length, controls the separation of scales and makes interface motion singularly slow. The load-bearing identity is the stationary-distribution representation (the Zubarev\u2013McLennan form) $P_{ss}\propto e^{\tilde S/\eta^3}$, where the modified entropy $\tilde S = S + J I$ contains the time-integrated excess entropy production $I$ during relaxation of an interface configuration. The paper evaluates $I$ by splitting it into bulk and interface contributions; the interface contribution uses a phenomenological Onsager law for energy exchange between the interface and the two bulk regions with coefficients $L_o = \lambda_o/(g X_-)$ and $L_d = \lambda_d/(g(1-X_+))$, and the condition that the inverse-temperature gap vanish as the interface approaches either boundary fixes $g=1/3$. Maximizing $\tilde S$ over interface position $X$ produces the variational equation whose solution is the interface temperature formula.

What would settle it

A direct test is a numerical simulation of the stochastic model (II.65)\u2013(II.67) under the non-equilibrium adiabatic condition for a first-order order-disorder transition with unequal bulk conductivities: measure the steady interface temperature $\theta^*$ and check whether $\theta^*-T_c$ equals $-(J/3)(1/\kappa_o-1/\kappa_d)X_{eq}(1-X_{eq})$, in particular whether the deviation is linear in $J$, vanishes when $\kappa_o=\kappa_d$, and changes sign when the conductivity ordering is reversed. An independent check is a molecular-dynamics simulation of phase coexistence under a heat flux measuring the local temperature profile near the interface to see a superheated ordered or supercooled disordered layer of the predicted magnitude.

Watch

Extended reading notes

Core claim

The central claim is that interface fluctuations, not deterministic bulk transport, set the coexistence temperature in steady heat conduction. The paper derives, within the linear response regime, the formula $\theta^* - T_c = -(J/3)(1/\kappa_o - 1/\kappa_d)X_{eq}(1-X_{eq})$, with $X_{eq}$ the equilibrium interface position, $\kappa_o$ and $\kappa_d$ the thermal conductivities of the ordered and disordered phases, and $J$ the heat flux ($J<0$ in the setup). Equivalently, for either sign of $J$, $\theta^* - T_c = |J|/3(1/\kappa_o - 1/\kappa_d)X_{eq}(1-X_{eq})$. The derivation proceeds by writing the stationary distribution of interface configurations through a modified entropy that includes the excess entropy produced during relaxation, decomposing that excess entropy into ordered-region, disordered-region, and interface parts, and maximizing the resulting potential over the interface position. The qualitative phenomenon\u2014superheated ordered or supercooled disordered states near the interface\u2014was predicted earlier by an extended thermodynamics framework; here it is obtained as the variational solution of a stochastic order parameter model, with a numerical prefactor $1/3$ instead of the earlier $1/2$.

Load-bearing premise

The load-bearing premise is that the energy exchange between the thin interface region and the two bulk regions is described by the phenomenological Onsager law (V.7)\u2013(V.10) with coefficients $L_o = \lambda_o/(g X_-)$ and $L_d = \lambda_d/(g(1-X_+))$, an uncontrolled approximation not yet derived from the stochastic model, and the factor $g=1/3$ is fixed by requiring the inverse-temperature gap to vanish at the boundaries.

Editorial extensions

If this is right

  • For a first-order order\u2013disorder transition under steady heat flux, the coexistence line is not at $T_c$: the interface temperature shifts linearly with $J$, so measured phase diagrams in a thermal gradient should show a shifted apparent transition temperature at the interface.
  • The sign of the shift is controlled by which phase conducts better: with the ordered phase less conductive, the ordered side is superheated; with the ordered phase more conductive, the disordered side is supercooled.
  • The deviation vanishes when the two bulk conductivities are equal, so unequal conductivities are necessary for the effect; it also vanishes as the interface approaches either boundary, consistent with the boundary fixing of $g=1/3$.
  • The deterministic, noiseless limit of the model predicts $\theta^*=T_c$, so the effect is carried by interface fluctuations: any coarse-grained description that omits the stochastic coupling of the interface to the bulk energy reservoirs would miss the shift.
  • The variational potential $V(X)$ provides a way to compute other non-equilibrium thermodynamic properties of coexistence, such as the most probable interface position, once the stationary distribution of interface configurations is known.

Reading between the lines

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

  • Because the authors conjecture the interface temperature is independent of the boundary condition for fixed energy and flux, the formula should also apply to the more standard setup of heat baths at the two ends; testing this in simulations would strengthen or falsify the conjecture.
  • The numerical factor $1/3$, fixed by requiring the temperature gap to vanish at the boundaries, is likely the least secure part of the argument; a microscopic derivation of the Onsager coefficients $L_o,L_d$ from the stochastic model would either confirm $1/3$ or replace it, while the qualitative sign of the interface-temperature shift would probably survive.
  • The same mechanism\u2014latent heat released by a fluctuating interface acting as a local heat source\u2014should appear in other first-order transitions such as liquid\u2013gas or nematic\u2013isotropic, with a conserved density adding an extra contribution; the paper mentions liquid\u2013gas as a natural next case.
  • A direct numerical check of the stochastic model could measure the inverse-temperature gap during interface relaxation and compare it with the prediction $\beta_+^{int}-\beta_-^{int} = (1/3)(1/\lambda_o-1/\lambda_d)(dX/dt)X(1-X)q_X$, isolating the coefficient $1/3$.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The manuscript constructs a stochastic order-parameter model for a Z2 order-disorder transition coupled to heat conduction, and imposes a non-equilibrium adiabatic boundary condition in which the boundary energy flux is fixed while total energy is conserved. From the Zubarev-McLennan representation the authors derive a stationary distribution for single-interface configurations, decompose the excess entropy production into ordered-bulk, disordered-bulk, and interface contributions, and evaluate the bulk contributions from deterministic relaxation while estimating the interface contribution with a projected Onsager description. The resulting potential function V(X;E,J) leads to the main result (VI.40), θ*−Tc = −(J/3)(1/κ_o−1/κ_d) X_eq(1−X_eq), predicting a superheated ordered interface when κ_d>κ_o and a supercooled disordered interface when κ_d<κ_o, in qualitative agreement with the authors' earlier global thermodynamics.

Significance. The bulk calculation is clean and the variational structure is transparent; deriving a variational principle for phase coexistence under heat flow from a stochastic model would be a significant conceptual advance. The authors are explicitly honest about the weak point: in Sec. V A they state that Eqs. (V.7)–(V.10) "involve uncontrolled approximations" and are "not yet derived from the stochastic model." Because the entire numerical coefficient 1/3 in (VI.40) is fixed through this uncontrolled step and through the boundary-condition choice g=1/3, the paper at present establishes the qualitative sign of the effect but not the quantitative prediction. I regard this as a valuable framework whose headline claim needs either additional derivation or an explicit downgrading to a conjecture.

major comments (2)
  1. [Sec. V A, Eqs. (V.7)–(V.10), (V.52)–(V.54), and (VI.40)] The central quantitative result (VI.40) is carried by the interface contribution I_int, whose evaluation in Sec. V A rests on the phenomenological Onsager description (V.7)–(V.10) with diagonal coefficients L_o=λ_o/(g X_-) and L_d=λ_d/(g(1−X_+)). The authors themselves state that this description involves uncontrolled approximations and has not been derived from the stochastic model. The value g=1/3 is then imposed by requiring β_+^int−β_-^int to vanish as X→0 and X→1, not derived. If the true interface contribution differs (for example, if off-diagonal Onsager terms contribute, or if g depends on X), the coefficient multiplying J(1/κ_o−1/κ_d)X(1−X) changes: with no interface contribution it is 0, and the independent global-thermodynamics estimate is 1/2. Thus the numerical coefficient, which is the quantitative content of (VI.40), is not established. I recommend either deriving the interface contribution from the stochastic model or explicitly presenting (VI.40) as a qualitative/conjectural prediction and marking the 1/3 factor as a model-dependent estimate.
  2. [Sec. VI A, Eqs. (VI.1)–(VI.3)] The variational principle is introduced through the ansatz P(X;E,J)=exp([V(X;E,J)+O(√η)]/η^3) and the identification V(X;E,J)=max_{α_X∈C_X} \tilde S(α_X;E,J), which the authors describe only as a "reasonable conjecture." Since all subsequent equations in Sec. VI are manipulations of this V, the claim in the abstract that a variational principle is "derived" from the stochastic model goes beyond what is actually shown. This step should either be justified (at least to the same standard as the bulk contribution) or be stated explicitly as an unproved assumption of the framework.
minor comments (4)
  1. [Eq. (VI.32)] The definition f_d(θ_X)=u_o(θ_X)−θ_X s_d(θ_X) appears to contain a typo: the disordered free-energy density should use u_d(θ_X), not u_o(θ_X). As written, the combination f_o−f_d in (VI.37) and the subsequent derivation of (VI.38)–(VI.40) are confusing.
  2. [Caption of Fig. 1 and Sec. II E] The figure caption states J<0 while the text states J≤0. This is harmless but should be made consistent.
  3. [Sec. VI E] The sentence comparing the factor 1/3 with the factor 1/2 from global thermodynamics would be more useful with a specific equation reference to Ref. [17], so that readers can verify the comparison.
  4. [Author affiliation] There are minor typographical errors in the affiliation and email lines, e.g., "J apan" and "r nakayama@tohoku.ac.jp"; these should be corrected in the final version.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central interface-temperature formula is derived from the stochastic model plus an explicitly phenomenological interface step, and the cited prior predictions are used only for comparison.

full rationale

The paper's central formula (VI.40) is not an input; it is the output of a chain that starts from the stochastic model (II.65)-(II.67), derives the Zubarev-McLennan stationary distribution (IV.7) and the modified entropy, computes the bulk excess-entropy-production terms (IV.47), and adds an interface term. The coefficient 1/3 enters through the phenomenological Onsager step (V.7)-(V.10): the parameter g is set to 1/3 by the boundary condition that the inverse-temperature gap vanish when the interface approaches the system boundaries (V.52)-(V.53). The authors explicitly state in Sec. V A that this description 'involves uncontrolled approximations' and is 'not yet derived from the stochastic model.' That is a serious limitation on the derivation's rigor and makes the quantitative coefficient conditional on a modeling assumption; it is not, however, circular, because the final temperature shift is not assumed at the outset, fitted to data, or obtained by renaming the prior thermodynamics result. The self-citations to the earlier prediction [16,17] are used for motivation and comparison ('If the factor 1/3 were 1/2, the result (VI.40) would be equivalent to the quantitative prediction by global thermodynamics'), not as the load-bearing derivation. Hence no circular step is present; the appropriate finding is score 0.

Assumptions & free parameters 1 free parameters · 5 assumptions · 0 invented entities

The central claim rests on a mesoscopic stochastic model and several simplifying assumptions. The most consequential are the phenomenological Onsager description for interface-bulk energy exchange (which directly sets the 1/3 coefficient) and the assumption that the interface conductivity is O(√η). No genuinely new physical entity is postulated. The free parameter g is the only adjustable number, fixed by a boundary condition rather than by microscopic derivation.

free parameters (1)
  • g = 1/3
    Dimensionless factor in the Onsager coefficients L_o = λ_o/(g X_-) and L_d = λ_d/(g(1-X_+)), introduced in equations (V.9)-(V.10). It is fixed to 1/3 by imposing that the inverse-temperature gap vanishes as X→0 and X→1 (Sec. V C). This is a hand-set constraint, not a derivation from the stochastic model, and it directly controls the coefficient 1/3 in the main result (VI.40).
assumptions (5)
  • domain assumption A mesoscopic entropy functional S(m,u) = ∫ [s(u,m) - (d_s/2)|∇m|^2] with mean-field entropy density and no nucleation events.
    The paper uses this entropy functional as the starting point (II.8), noting it is a 'good starting hypothesis' rather than derived from microscopic principles.
  • domain assumption The stochastic dynamics (II.65)-(II.67) with Gaussian white noise satisfying detailed balance and the non-equilibrium adiabatic boundary condition (II.73)-(II.74).
    This is the model definition. The noise requires a cutoff Λ_c as discussed in Appendix B, and the formal model is justified by the physical model with finite cutoff.
  • domain assumption The stationary distribution has the Zubarev-McLennan form P_ss ∝ e^{S̃/η^3} with S̃ expanded to linear order in J.
    Assumed after (IV.6)-(IV.8). It is supported by a local detailed balance argument in Appendix C, but the limiting procedures (η→0, K→∞, ǫ→0) are assumptions about the separation of scales.
  • ad hoc to paper In the interface region the thermal conductivity λ is O(√η) and its functional form is not specified (IV.19)-(IV.20).
    This is a key modeling assumption enabling the temperature gap. It is argued from fluctuation scaling in Sec. III C but is not derived from the microscopic stochastic model.
  • ad hoc to paper The Onsager description of energy exchange between interface and bulk regions, equations (V.7)-(V.10), with diagonal coefficients only and L_o = λ_o/(g X_-), L_d = λ_d/(g(1-X_+)).
    The paper states this description 'involves uncontrolled approximations' and is 'not yet derived from the stochastic model'. The central coefficient 1/3 depends on it.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Stochastic order parameter dynamics for phase coexistence in heat conduction." pith.science (2026). https://pith.science/paper/7W3EIUUW

@misc{pith2026190803029,
  author       = {Pith},
  title        = {Pith review of: Stochastic order parameter dynamics for phase coexistence in heat conduction},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7W3EIUUW}},
  note         = {Machine review of arXiv:1908.03029}
}
read the original abstract

We propose a stochastic order parameter equation for describing phase coexistence in steady heat conduction near equilibrium. By analyzing the stochastic dynamics with a non-equilibrium adiabatic boundary condition, where total energy is conserved over time, we derive a variational principle that determines thermodynamic properties in non-equilibrium steady states. The resulting variational principle indicates that the temperature of the interface between the ordered region and the disordered region becomes greater (less) than the equilibrium transition temperature in the linear response regime when the thermal conductivity in the ordered region is less (greater) than that in the disordered region. This means that a super-heated ordered (super-cooled disordered) state appears near the interface, which was predicted by an extended framework of thermodynamics proposed in [N. Nakagawa and S.-i. Sasa, Liquid-gas transitions in steady heat conduction, Phys. Rev. Lett. {\bf 119}, 260602, (2017).]

Figures

Figures reproduced from arXiv: 1908.03029 by the authors.

Figure 1
Figure 1. FIG. 1. Schematic of setup. The configuration of a single [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Schematic graph of [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. The statistical average of a single interface is repr [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4. Schematic figure of a stationary interface in equilib [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Example of the graph [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Space-time plot associated with interface motion [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7. Coarse-grained description for determining the tem [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Temperature configuration in the late stage of a re [PITH_FULL_IMAGE:figures/full_fig_p016_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Temperature profile [PITH_FULL_IMAGE:figures/full_fig_p019_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Schematic of the main result [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. Free energy as a function of [PITH_FULL_IMAGE:figures/full_fig_p023_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12 [PITH_FULL_IMAGE:figures/full_fig_p024_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13. Schematic figure of non-local Onsager coefficient [PITH_FULL_IMAGE:figures/full_fig_p026_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14. Schematic figure of interface motion from the quasi [PITH_FULL_IMAGE:figures/full_fig_p028_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 76 canonical work pages

  1. [1]

    inverse-temperature gap

    We also impose that the interface configuration satis- fies |¯v(x)| ≤ δv, (IV.18) where the constant δv is much smaller than 1. Since we consider the limit η → 0, the final result is independent of the parameters ( δm,δ v,r ). For a given single interface configuration αX , we study the time evolution from αX . We assume that a config- uration at any time t in...

  2. [2]

    Here, a1,a2,a3, and T0 are positive constants

    Landau theory We start with a Landau free energy density f (T,m ) = a1 2 (T −T0)m2 −a2 4 m4 +a3 6 m6 +ϕ(T ), (A.1) which describes the first order transition at some temper- atureTc. Here, a1,a2,a3, and T0 are positive constants. The functional form of ϕ(T ) will be determined later. See (A.16). For a given T , the equilibrium value meq(T ) ≥ 0 is determin...

  3. [3]

    Ben-Jacob and P

    E. Ben-Jacob and P. Garik, The formation of patterns in nonequilibrium growth, Nature 343, 523-530 (1990)

    work page 1990

  4. [4]

    (A.13) 24 − m loc (T ) m loc (T ) m T T 1 T 0 m 1 T FIG

    Entropy density The entropy density s(T,m ) is given by s = − ( ∂f ∂T ) m (A.12) = −a1 2 m2 −ϕ′(T ). (A.13) 24 − m loc (T ) m loc (T ) m T T 1 T 0 m 1 T FIG. 12. T (m) as a function of m. The internal energy density u(T,m ) is determined as u(T,m ) = −a1 2 T0m2 − a2 4 m4 + a3 6 m6 +ϕ(T ) −Tϕ ′(T ). (A.14) For simplicity, we assume that the heat capacity p...

    work page 1970

  5. [5]

    The key concept here is to introduce q by φ = E LLyLz + ∇q, (B.1) where we impose qn = 0 at the boundaries so as to satisfy (II.19)

    Preliminaries for the derivation In order to derive the stochastic model, we rewrite the set of deterministic equations, (II.31), (II.32), and (II.33), as the simplest form. The key concept here is to introduce q by φ = E LLyLz + ∇q, (B.1) where we impose qn = 0 at the boundaries so as to satisfy (II.19). We express (B.1) as φ =φ(q). We here note S(m,v,φ ...

    work page

  6. [6]

    Derivation Since we assume the cut-off length in the noise, (B.12) becomes a non-local form with using a functional of χ as Lab(χ; r, r′) ≡ ∫ d3r′′Lab(χ(r′′), ∇χ(r′′)) ×δΛ c(r − r′′)δΛ c (r′ − r′′), (B.20) which is illustrated in Fig. 13. Further, since the On- sager coefficients Lab in (B.10) depend on χ, we have to consider multiplicative nature of the noi...

    work page

  7. [7]

    H. B. Callen, Thermodynamics and an Introduction to Thermostatistics, 2nd ed. (Wiley, New York, 1985)

    work page 1985

  8. [8]

    J. R. Thome, Boiling in microchannels: a review of exper- iment and theory, Int. J. Heat and Fluid flow 25, 128-139 (2004)

    work page 2004

Show all 82 references
  1. [9]

    D. M. Anderson, G. B. McFadden, and A. A. Wheeler, Diffuse-interface methods in fluid mechanics, Annual Re- view of Fluid Mechanics 30, 139-165 (1998)

    1998

  2. [10]

    Ahlers, L

    G. Ahlers, L. I. Berge, and D. S. Cannell, Thermal con- vection in the presence of a first-order phase change, Phys. Rev. Lett. 70, 2399 (1993)

    1993

  3. [11]

    Zhong, D

    J.-Q. Zhong, D. Funfschilling, and G. Ahlers, Enhanced heat transport by turbulent two-phase Rayleigh-Benard convection, Phys. Rev. Lett. 102, 124501 (2009)

    2009

  4. [12]

    In order to seek the solutions, we consider a1T ′(m) = 2a2m − 4a3m3 = 0, (A.8) which gives m = 0 and m = ±m1 with m1 = √ a2 2a3 . (A.9) By setting T1 =T (m1) = T0 + a2 2 4a1a3 , (A.10) we find three locally stable states m = 0 and m = ±mloc(T ) when T0 ≤ T ≤ T1, where mloc(T ) ...

  5. [13]

    Weiss and G

    S. Weiss and G. Ahlers, Nematic-isotropic phase transi- tion in turbulent thermal convection, J. Fluid Mech. 737, 308-328 (2013)

    2013

  6. [14]

    M. E. Cates and J. Tailleur, Motility-Induced Phase Sep- aration, Annual Review of Condensed Matter Physics 6, 219-244 (2015)

    2015

  7. [15]

    Urbana, D

    P. Urbana, D. Schmoranzerb, P. Hanzelkaa, K. R. Sreeni- vasanc, and L. Skrbekb, Anomalous heat transport and condensation in convection of cryogenic helium, Proc. Nat. Acad. Sci. 110, 8036-8039 (2013)

    2013

  8. [16]

    Bedeaux, E

    D. Bedeaux, E. Johannessen, and A. Røsjorde, The nonequilibrium van der Waals square gradient model.(I). The model and its numerical solution, Physica A 330, 329-353 (2003)

    2003

  9. [17]

    Onuki, Dynamic van der Waals theory, Phys

    A. Onuki, Dynamic van der Waals theory, Phys. Rev. E 75, 036304 (2007)

    2007

  10. [18]

    Schmitz, Fluctuations in nonequilibrium fluids, Physics Reports 171, 1-58 (1988)

    R. Schmitz, Fluctuations in nonequilibrium fluids, Physics Reports 171, 1-58 (1988)

    1988

  11. [19]

    Bertini, A

    L. Bertini, A. De Sole, D. Gabrielli, G. Jona-Lasinio, a nd C. Landim, Macroscopic fluctuation theory, Rev. Mod. Phys. 87, 593 (2015)

    2015

  12. [20]

    Forster, D

    D. Forster, D. R. Nelson, and M. J. Stephen, Large- distance and long-time properties of a randomly stirred fluid, Phys. Rev. A 16, 732 (1977)

    1977

  13. [21]

    Hohenberg and B

    P.C. Hohenberg and B. I. Halperin, Theory of dynamic critical phenomena, Rev. Mod. Phys. 49 435-479 (1977)

    1977

  14. [22]

    Nakagawa and S.-i

    N. Nakagawa and S.-i. Sasa, Liquid-gas transitions in steady heat conduction, Phys. Rev. Lett. 119, 260602 (2017)

    2017

  15. [23]

    Nakagawa and S.-i

    N. Nakagawa and S.-i. Sasa, Global thermodynamics for heat conduction states, J. Stat. Phys. 177, 825-888 (2019)

    2019

  16. [24]

    E. F. Gramsbergen, L. Longa, and W.H. de Jeu, Landau theory of the nematic-isotropic phase transition, Physics Report 135, 195-257 (1986)

    1986

  17. [25]

    Sekimoto, Stochastic Energetics , Lect

    K. Sekimoto, Stochastic Energetics , Lect. Notes Phys. 799 (Springer-Verlag, Berlin, 2010)

    2010

  18. [26]

    Seifert, Stochastic thermodynamics, fluctuation th e- orems and molecular machines, Rep

    U. Seifert, Stochastic thermodynamics, fluctuation th e- orems and molecular machines, Rep. Prog. Phys. 75, 126001 (2012)

    2012

  19. [27]

    D. J. Evans, E. G. D. Cohen, G. P. Morriss, Probability of second law violations in shearing steady states, Phys. Rev. Lett. 71, 2401–2404 (1993)

    1993

  20. [28]

    Gallavotti and E

    G. Gallavotti and E. G. D. Cohen, Dynamical Ensem- bles in Nonequilibrium Statistical Mechanics, Phys. Rev. Lett. 74, 2694 (1995)

    1995

  21. [29]

    Kurchan, Fluctuation theorem for stochastic dynam- ics, J

    J. Kurchan, Fluctuation theorem for stochastic dynam- ics, J. Phys. A: Math. Gen. 31, 3719 (1998)

    1998

  22. [30]

    J. L. Lebowitz and H. Spohn, A Gallavotti–Cohen-type symmetry in the large deviation functional for stochastic dynamics, J. Stat. Phys. 95, 333 (1999)

    1999

  23. [31]

    Maes, The fluctuation theorem as a Gibbs property, J

    C. Maes, The fluctuation theorem as a Gibbs property, J. Stat. Phys. 95, 367-392 (1999)

    1999

  24. [32]

    G. E. Crooks, Entropy production fluctuation theorem and the nonequilibrium work relation for free energy dif- ferences, Phys. Rev. E 60, 2721 (1999)

    1999

  25. [33]

    Jarzynski, Nonequilibrium equality for free energy dif- ferences, Phys

    C. Jarzynski, Nonequilibrium equality for free energy dif- ferences, Phys. Rev. Lett. 78, 2690–2693 (1997)

    1997

  26. [34]

    Sasa, Derivation of hydrodynamics from the Hamil - tonian description of particle systems, Phys

    S.-i. Sasa, Derivation of hydrodynamics from the Hamil - tonian description of particle systems, Phys. Rev. Lett. 112, 100602 (2014)

    2014

  27. [35]

    Sasa, Collective dynamics from stochastic therm o- dynamics, New Journal of Physics 17, 045024 (2015)

    S.-i. Sasa, Collective dynamics from stochastic therm o- dynamics, New Journal of Physics 17, 045024 (2015)

    2015

  28. [36]

    D. N. Zubarev, Nonequilibrium Statistical Thermody- namics, (Consultants Bureau, New York, 1974)

    1974

  29. [37]

    J. A. Mclennan, Phys. Fluids 3, 493 (1960); Introduction to Non-equilibrium Statistical Mechanics (Prentice-Hall, 1988)

    1960

  30. [38]

    T. S. Komatsu and N. Nakagawa, Expression for the stationary distribution in nonequilibrium steady states, Phys. Rev. Lett. 100, 030601 (2008)

    2008

  31. [39]

    T. S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki Representation of nonequilibrium steady states in large mechanical systems, J. Stat. Phys. 134, 401-423 (2009)

    2009

  32. [40]

    Maes and K

    C. Maes and K. Netoˇ cn´ y, Rigorous meaning of McLennan ensembles, J. Math. Phys. 51, 015219 (2010)

    2010

  33. [41]

    Fang and C

    G. Fang and C. A. Ward, Temperature measured close to the interface of an evaporating liquid, Phys. Rev. E 59, 417-428 (1999)

    1999

  34. [42]

    E. T. Jaynes, The minimum entropy production princi- 31 ple, Ann. Rev. Phys. Chem. 31, 579- 601 (1980)

    1980

  35. [43]

    M. J. Klein and P. H. E. Meijer, Principle of minimum entropy production, Phys. Rev. 96, 250-255 (1954)

    1954

  36. [44]

    Maes and K

    C. Maes and K. Netoˇ cn´ y, Minimum entropy produc- tion principle from a dynamical fluctuation law, J. Math. Phys. 48, 053306 (2007)

    2007

  37. [45]

    Derrida, Non-equilibrium steady states: fluctuatio ns and large deviations of the density and of the current, J

    B. Derrida, Non-equilibrium steady states: fluctuatio ns and large deviations of the density and of the current, J. Stat. Mech. P07023 (2007)

    2007

  38. [46]

    Nemoto and S.-i

    T. Nemoto and S.-i. Sasa, Thermodynamic formula for the cumulant generating function of time-averaged cur- rent, Phys. Rev. E 84, 061113 (2011)

    2011

  39. [47]

    J. L. Lebowitz, E. Presutti, H. Spohn, Microscopic Mod- els of Hydrodynamic Behavior, J. Stat. Phys. 51, 841 (1988)

    1988

  40. [48]

    L. D. Landau and E. M. Lifshitz, Fluid Mechanics, (Perg- amon Press, Oxford 1959)

    1959

  41. [49]

    B. I. Halperin, P.C. Hohenberg, and S. K. Ma, Renormal- ization group methods for critical dynamics I. Recursion relations and effects of energy conservation, Phys. Rev. B 10 139-153, (1974)

    1974

  42. [50]

    Penrose and P

    O. Penrose and P. C. Fife, Thermodynamically consis- tent models of phase-field type for the kinetic of phase transitions, Physica D 43, 44-62 (1990)

    1990

  43. [51]

    Fujitani, Perturbation calculation for the density pro- file across the flat liquid-vapor interface in the steady heat-flow state, J

    Y. Fujitani, Perturbation calculation for the density pro- file across the flat liquid-vapor interface in the steady heat-flow state, J. Phys. Soc. Jpn. 79, 074002 (2010)

    2010

  44. [52]

    Fukuma and Y

    M. Fukuma and Y. Sakatani, Entropic formulation of rel- ativistic continuum mechanics, Phys. Rev. E 84, 026315 (2011)

    2011

  45. [53]

    R. M. Townsend and S. A. Rice, Molecular dynamics studies of the liquid-vapor interface of water, J. Chem. Phys. 94, 2207 (1991)

    1991

  46. [54]

    D. G. Triezenberg and R. Zwanzig, Fluctuation theory of surface tension, Phys. Rev. Lett. 28 1183-1185 (1972)

    1972

  47. [55]

    Weeks, Structure and thermodynamics of the liquid - vapor interface, J

    J.D. Weeks, Structure and thermodynamics of the liquid - vapor interface, J. Chem. Phys. 67 3106 (1977)

    1977

  48. [56]

    R. P. Feynman, R. B. Leighton, and M. Sands, The Feyn- manLectures on Physics , Vol. I (Addison-Wesley, Read- ing, Mas-sachusetts, 1963) Chap. 39-4

    1963

  49. [57]

    E. H. Lieb, Some problems in statistical mechanics that I would like to see solved, Physica A 263, 491 (1999)

    1999

  50. [58]

    Gruber and J

    C. Gruber and J. Piasecki, Stationary motion of the adi- abaticpiston, Physica A 268, 412 (1999)

    1999

  51. [59]

    Gruber and L

    C. Gruber and L. Frachebourg, On the adiabatic proper- ties of a stochastic adiabatic wall: Evolution, stationary non-equilibrium, and equilibrium states, Physica A 272, 392 (1999)

    1999

  52. [60]

    Hatano and S.-i

    T. Hatano and S.-i. Sasa, Steady-state thermodynam- ics of Langevin systems, Phys. Rev. Lett. 86, 3463–3466 (2001)

    2001

  53. [61]

    T. S. Komatsu, N. Nakagawa, S.-i. Sasa, and H. Tasaki, Steady-state thermodynamics for heat conduction: Mi- croscopic derivation, Phys. Rev. Lett. 100, 230602 (2008)

    2008

  54. [62]

    Nakagawa, Work relation and the second law of ther- modynamics in nonequilibrium steady states, Phys

    N. Nakagawa, Work relation and the second law of ther- modynamics in nonequilibrium steady states, Phys. Rev. E 85, 051115 (2012)

    2012

  55. [63]

    Bertini, D

    L. Bertini, D. Gabrielli, G. Jona-Lasinio, and C. Landi m, Clausius inequality and optimality of quasistatic trans- formations for nonequilibrium stationary states, Phys. Rev. Lett. 110, 020601 (2013)

    2013

  56. [64]

    Maes and K

    C. Maes and K. Netoˇ cn´ y, A nonequilibrium extension of the Clausius heat theorem, J. Stat. Phys. 154, 188-203 (2014)

    2014

  57. [65]

    Chiba and N

    Y. Chiba and N. Nakagawa, Numerical determination of entropy associated with excess heat in steady-state ther- modynamics, Phys. Rev. E 94, 022115 (2016)

    2016

  58. [66]

    Keizer, Thermodynamics at nonequilibrium steady states, J

    J. Keizer, Thermodynamics at nonequilibrium steady states, J. Chem. Phys. 69, 2609 (1978)

    1978

  59. [67]

    B. C. Eu, Irreversible thermodynamics of fluids, Annals of Physics 140, 341-371 (1982)

    1982

  60. [68]

    D. Jou, J. Casas-V´ azquez, and G. Lebon, Extended ir- reversible thermodynamics, Rep. Prog. Phys. 51, 1105- 1179 (1988)

    1988

  61. [69]

    Oono and M

    Y. Oono and M. Paniconi, Steady state thermodynamics, Prog. Theor. Phys. Suppl. 130, 29 (1998)

    1998

  62. [70]

    Sasa and H

    S.-i. Sasa and H. Tasaki, Steady state thermodynamics, J. Stat. Phys. 125, 125–224 (2006)

    2006

  63. [71]

    Bertin, K

    E. Bertin, K. Martens, O. Dauchot, and M. Droz, Inten- sive thermodynamic parameters in nonequilibrium sys- tems, Phys. Rev. E 75, 031120 (2007)

    2007

  64. [72]

    Pradhan, R

    P. Pradhan, R. Ramsperger, and U. Seifert, Approximate thermodynamic structure for driven lattice gases in con- tact, Phys. Rev. E 84, 041104 (2011)

    2011

  65. [73]

    Dickman, Failure of steady-state thermodynamics in nonuniform driven lattice gases, Phys

    R. Dickman, Failure of steady-state thermodynamics in nonuniform driven lattice gases, Phys. Rev. E 90, 062123 (2014)

    2014

  66. [74]

    Røsjorde, D

    A. Røsjorde, D. W. Fossmo, D. Bedeaux, S. Kjelstrup, and B. Hafskjold, Nonequilibrium molecular dynamics simulations of steady-state heat and mass transport in condensation: I. Local equilibrium, J. Coll. Int. Sci. 232, 178-185 (2000)

    2000

  67. [75]

    Ogushi, S

    F. Ogushi, S. Yukawa, and N. Ito, Asymmetric struc- ture of gas-liquid interface, J. Phys. Soc. Jpn. 75, 07301- (2006)

    2006

  68. [76]

    D. N. Zubarev and V. G. Morozov, Statistical mechanics of nonlinear hydrodynamic fluctuations, Physica 120A, 411-467 (1983)

    1983

  69. [77]

    V. G. Morozov, On the Langevin formalism for nonlinear and nonequilibrium hydrodynamic fluctuations, Physica 126A, 443-460 (1984)

    1984

  70. [78]

    Graham and H

    R. Graham and H. Haken, Fluctuations and stability of stationary non-equilibrium systems in detailed balance, Z. Phys. 245, 141-153 (1971)

    1971

  71. [79]

    Zwanzig, Memory effects in irreversible thermody- namics, Phys

    R. Zwanzig, Memory effects in irreversible thermody- namics, Phys. Rev. 124, 983-992 (1961)

    1961

  72. [80]

    Itami and S.-i

    M. Itami and S.-i. Sasa, Universal form of stochastic ev o- lution for slow variables in equilibrium systems, J. Stat. Phys. 167, 46-63 (2017)

    2017

  73. [81]

    Nakano and S.-i

    H. Nakano and S.-i. Sasa, Statistical mechanical expre s- sions of slip length, J. Stat. Phys. 176, 312-357 (2019)

    2019

  74. [82]

    Pomeasu, Front motion, metastability and subcritic al bifurcations in hydrodynamics, Physica 23D, 3-11 (1986)

    Y. Pomeasu, Front motion, metastability and subcritic al bifurcations in hydrodynamics, Physica 23D, 3-11 (1986)

    1986

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.