Pith. sign in

REVIEW 3 major objections 4 minor 69 references

Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems

T0 review · 3 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 Boundary heat flows from thermostatted walls yield Fourier's law and the McLennan-Zubarev steady state from first principles.

desk verdict The linear-response machinery from boundary thermostats to Green-Kubo is solid and worth engaging; the nonlinear McLennan-Zubarev derivation rests on an unproven fast-relaxation step that the author himself flags. read the letter →

arxiv 1908.07202 v1 pith:VDP5ODTZ submitted 2019-08-20 cond-mat.stat-mech cond-mat.soft

Akira Onuki This is my paper · ORCID
classification cond-mat.stat-mechcond-mat.soft PACS 44.10.+i05.60.-k05.70.Ln
keywords thermalconductivityGreen-KuboformulaboundarythermostatslinearresponsetheoryMcLennan-ZubarevdistributionfluctuationtheoremsNosé-Hooverthermostatsurface-to-bulkrelation
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

Onuki develops a microscopic statistical mechanics of heat conduction in a fluid film heated from thermostatted boundary walls, starting from the equations of motion rather than postulating a temperature profile. He shows that the linear response of any observable to a small boundary temperature change is fixed by equilibrium time-correlation functions between that observable and the heat flows from the two thermostats. A surface-to-bulk identity rewrites those wall heat flows as bulk space integrals, splitting the response into a local-equilibrium part and a dissipative part; the dissipative part yields Fourier's law with Green's expression for the thermal conductivity. In the nonlinear regime the same route delivers the steady-state phase-space distribution in the McLennan-Zubarev form, with a local-equilibrium distribution weighted by an integrated bulk heat-flux dissipation function, and several fluctuation theorems. If the derivation stands, it connects boundary-driven nonequilibrium simulations to bulk Green-Kubo transport coefficients.

What carries the argument

The load-bearing object is the surface-to-bulk relation in Eqs. (13) and (25), which writes each thermostat heat flow $J_K$ as a sum of a boundary-layer energy time-derivative, a time-derivative of an integral of the bulk heat variable $\hat q = \hat e - h\hat n$, and the integrated bulk heat flux $G(t)=\int dr J_z^h(r,t)$. This identity is what turns surface-driven linear response into bulk correlation functions: inserted into $\chi_{BK}(t)=\langle B(t)J_K(0)\rangle_e$, it produces the split into a local-equilibrium part (equal-time correlations with $\hat q$) and a dissipative part (time integral of $G$), whose long-time limit gives Green's formula for the thermal conductivity. The argument also relies on the fast-thermostat identification $J_K\simeq I_K$, meaning the Nosé-Hoover friction variable $\zeta_K$ relaxes on a time $\tau_h$ much shorter than bulk microscopic times, so that the thermostat heat flow equals the mechanical heat flow from the bound wall particles to the fluid.

What would settle it

Run a molecular-dynamics simulation of a Lennard-Jones fluid between two Nosé-Hoover thermostatted walls, measure the steady-state heat flux and temperature gradient to obtain $\lambda$ directly, and separately compute the equilibrium time-correlation integral in Eq. (45) from the wall heat flows $J_K$ (or from the bulk flux $J_z^h$) over a range of thermostat times $\tau_h$. If the correlation-integral value disagrees with the direct $\lambda$ unless $\tau_h$ is artificially small, the fast-thermostat identification $J_K\simeq I_K$ and the surface-to-bulk reduction would be falsified for realistic thermostat parameters.

Watch

Extended reading notes

Core claim

The central claim is that all boundary-driven heat response in a classical fluid between Nosé-Hoover thermostatted walls is governed by the thermostat heat flows $J_K$ (with $K$ = top or bottom), defined as the energy per time delivered from each thermostat to the particles. In the linear regime the deviation of any variable $B$ is $\delta\bar B(t) = -\int_0^t ds\,\sum_K \chi_{BK}(s)\,\delta\beta_K(t-s)$ with $\chi_{BK}(t)=\langle B(t)J_K(0)\rangle_e$. The key step is the surface-to-bulk relation, $J_{\rm top}= d/dt[\int dr\,(z/H)\hat q + H_{\rm top}] - G/H$ and its mirror for the bottom, where $G(t)=\int dr J_z^h(r,t)$ is the integrated bulk heat flux; this converts wall quantities into bulk ones. The dissipative part of the response is proportional to $G$, and in the limit $t\to\infty$ its time integral yields Green's expression $\lambda = (1/V k_B T^2)\int_0^\infty dt\int dr\int dr'\,\langle J_z^h(r,t)J_z^h(r',0)\rangle_e$. In the nonlinear regime, the steady-state distribution takes the McLennan-Zubarev form $P_{\rm st}=P_{\rm lc}\exp[D(t_{\rm lc})]$, where $P_{\rm lc}$ is the local-equilibrium distribution built from a linear inverse-temperature profile and $D(t)$ is the integrated bulk heat-flux dissipation. The author also derives transient and steady fluctuation theorems, including the exact transient relation for stepwise boundary temperature changes.

Load-bearing premise

The identification $J_K \approx I_K$ (Eq. (34)) — that the thermostat relaxation time $\tau_h$ is much shorter than the microscopic bulk time and independent of temperature — is the load-bearing premise; if the thermostat is not fast enough, the response functions and the derived thermal-conductivity and steady-state formulas describe a different system than the actual thermostatted walls.

Editorial extensions

If this is right

  • If the derivation is right, the thermal conductivity of a fluid can be extracted from equilibrium correlations of the wall thermostat heat flows alone, giving a practical route that matches boundary-driven nonequilibrium simulations with bulk Green-Kubo theory.
  • Steady-state averages of hydrodynamic variables follow from a two-part formula: a local-equilibrium part set by equal-time canonical correlations, including long-range $V^{-1}$ terms that yield the constant-pressure temperature derivative, and a dissipative part tied to the heat-flux integral.
  • The nonlinear steady-state distribution is the McLennan-Zubarev form, so nonlinear corrections to transport coefficients can be computed starting from a temperature-profile-dependent local-equilibrium ensemble rather than from the equilibrium one.
  • The causality prediction $\chi_{aK}(z,t)=0$ for $0<ct<z$ and $H-z$ means thermal response appears in the interior only after sound arrival, a testable signal in simulations.

Reading between the lines

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

  • The same surface-to-bulk construction should extend to simultaneous heat and momentum boundary drives, yielding a unified derivation of Green-Kubo shear and bulk viscosities from wall force correlations; the paper develops only the thermal case and cites the shear analogue.
  • If the thermostat relaxation time is not short compared with bulk microscopic times, Eq. (48) provides a correction term in $J'_K$; one could test numerically whether using $J'_K$ restores the Green-Kubo value of $\lambda$ when $\tau_h$ is varied over a range.
  • The local-equilibrium weight $\exp[D(t)]$ is expressed solely through the integrated bulk heat flux, suggesting that for coarse-grained or multi-component descriptions the same entropy-production functional controls the steady-state ensemble; this is an extension beyond the one-component film treated here.
  • Near the critical point, where the piston effect makes adiabatic heating large, the separation of time scales $t_1 \ll t_D$ in the dissipation function could be measured directly in experiments or simulations to test the hydrodynamic part of the calculation.
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

3 major / 4 minor

Summary. The paper constructs a microscopic theory of heat flow in a classical fluid confined between Nosé-Hoover thermostatted boundary walls. In the linear regime it derives a response formula, Eq. (41), expressing the deviation of any observable in terms of equilibrium time-correlation functions with the thermostat heat flows J_K, and uses the surface-to-bulk identities of Eq. (25) to rewrite the response in a bulk form whose dissipative part yields Green's expression for the thermal conductivity, Eq. (45). In the nonlinear regime the paper derives a phase-space dissipation function, presents fluctuation theorems, and claims a first-principles derivation of a McLennan-Zubarev-type steady-state distribution, Eqs. (122)-(123), starting from a local-equilibrium distribution P_lc. The paper also provides hydrodynamic calculations of the relaxation after a boundary temperature change and a canonical-ensemble analysis of long-range correlations.

Significance. If the results hold, the paper establishes a clean formal link between boundary-driven nonequilibrium molecular dynamics and bulk Green-Kubo transport coefficients, and it gives a microscopic route to the McLennan-Zubarev steady-state form. The linear-response part is elegant: Eq. (41) follows from the linearized Liouville equation, and Eq. (25) is an exact surface-to-bulk identity. The causality prediction in Eq. (47) is a falsifiable statement that could be tested numerically. The nonlinear steady-state claim, however, rests on an unproven relaxation assumption, so the paper's strongest claim is not yet fully supported.

major comments (3)
  1. [Section IV E, Eqs. (122)-(123) and Remark (6)] The central nonlinear claim P_st(Γ) = P_lc(Γ) exp[D(t_lc)] is not established. The argument relies on the assertion that P_lc relaxes to the steady state in a microscopic time, but no proof, timescale estimate, or numerical evidence is provided. This matters because D(t) = -γ_a ∫_0^t ds G(-s) is a time integral of the boundary heat flux whose steady-state mean is nonzero; hence exp[D(t_lc)] depends on the arbitrarily chosen t_lc unless a convergent regularization is employed, and the equivalence of Eqs. (125)-(126) to the unregularized form is not shown. The paper's own Remark (6) asks for a numerical study of the P_lc → P_st relaxation, effectively conceding that the necessary support is missing. Without this support, the claim of a first-principles derivation of the McLennan-Zubarev form should be softened to a conjecture or the required relaxation argument must be supplied.
  2. [Section III C, Eqs. (63)-(66) and Appendix A] The boundary-fluctuation formula for the thermal conductivity, Eq. (66), is derived from the hydrodynamic solution in Appendix A, which starts from the heat equation (A1) with a given conductivity λ. Consequently, Eq. (66) follows from an input that already contains λ and cannot serve as an independent derivation of λ from boundary fluctuations. This circularity does not affect the main Green-Kubo expression, Eq. (45), which is obtained directly from the linear-response calculation and the surface-to-bulk identity, but the text should explicitly identify Eq. (66) as a consistency check of the hydrodynamic description rather than a microscopic derivation.
  3. [Section IV D, Eqs. (112)-(114)] The nonlinear analysis assumes a linear inverse-temperature profile δβ̄(z) = δβ_bot − γ_a z in Eq. (113), and this profile is used to define both the local-equilibrium distribution P_lc(Γ) in Eq. (114) and the dissipation function D(t) in Eq. (112). For large boundary temperature differences, the steady-state temperature profile is generally nonlinear when transport coefficients depend on temperature. The paper does not state the regime of validity of the linear-profile assumption in the nonlinear regime, nor does it generalize Ψ(Γ) to an arbitrary β(z). The claim that Eqs. (122)-(123) represent the steady-state distribution should be restricted to the linear-profile regime or generalized accordingly.
minor comments (4)
  1. [Throughout the text, Eqs. (48), (125)] There are several typographical errors: the running header contains 'Wa lls' and 'Fluctuat ion', the abstract contains 'quantiti es', Eq. (48) uses the notation 'ẋζ_K' where dζ_K/dt is intended, and Eq. (125) states 'ǫe^{-ǫt} = -d(e^{-ǫ})/dt' but the final exponential should be e^{-ǫt}. Please proofread carefully.
  2. [Section III A, after Eq. (42)] The statement that ⟨B(t)J_K(0)⟩_e is 'nearly equal' to ⟨B(t)I_K(0)⟩_e for t ≫ τ_h is an uncontrolled approximation. The main linear-response result in Eq. (41) and the Green-Kubo formula in Eq. (45) are exact in terms of J_K and do not depend on this identification; making that point explicit would prevent readers from believing the central results require the fast-thermostat assumption.
  3. [Reference list, Ref. [20]] Reference [20] contains a typo, 'Fourierfs law' instead of 'Fourier's law'.
  4. [Section IV E, Eqs. (119)-(121)] The switching between backward trajectories in Eq. (124) and forward trajectories in Eqs. (120) and (123) is somewhat terse; a short sentence explicitly listing which definition of D(t) and G(t) is used in each of Eqs. (119), (120), (121), and (125)-(126) would improve readability.

Circularity Check

1 steps flagged · score 2.0 of 10

Mostly self-contained: the linear-response chain to Green's expression for lambda (Eqs. 41, 25, 45) is non-circular; one side formula (Eq. 66) reuses lambda from hydrodynamics, and the nonlinear steady-state step relies on an unproven Plc-to-Pst relaxation timescale flagged in Remark (6).

  1. self definitional [Sec. III C, Eqs. (64)-(66); Appendix A, Eqs. (A1), (A3)]
    "In the limit t → ∞, Eq.(64) becomes ... In terms of Ja = (Jbot − Jtop)/2, we obtain the surface expression for λ derived by Petravic and Harrowell 19, λ = H/(k_B T^2 A) ∫_0^∞ dt⟨Ja(t)Ja(0)⟩e. ... These integral relations stem from the hydrodynamics. ... We start with the heat conduction equation nT ∂/∂t δs = λ∇_z^2 δT. ... Itop(t) = AλδT′(H,t)."

    Eq. (66) is presented as an expression for the thermal conductivity, but the correlation integrals in Eqs. (64)-(65) are computed from the hydrodynamic solution of Eq. (A1), in which λ is already the thermal conductivity, and from boundary fluxes written as AλδT′ in Eq. (A3). Substituting that λ-dependent solution back into Eq. (66) recovers the same λ, so the formula is a consistency relation between boundary-fluctuation correlations and the λ already assumed in the hydrodynamics, not an independent first-principles derivation. The paper itself acknowledges that these integral relations stem from the hydrodynamics. This circularity is side-located and non-load-bearing because the main Green-Kubo expression, Eq. (45), is derived separately from the exact surface-to-bulk relation, Eq.

full rationale

The central linear-response derivation is self-contained. Eq. (41) follows from the linearized Liouville equation with the thermostat perturbation δL, and Eq. (25) is an exact surface-to-bulk identity obtained from the equations of motion. The reduction to Green's expression for λ in Eq. (45) uses only Eq. (25) together with time-reversal stationarity to drop time-derivative correlation terms; it does not rely on the J_K ≈ I_K approximation or on the hydrodynamic solution in Appendix A. I therefore find no circularity in the main λ result. The one explicit circular reduction is the surface-fluctuation formula, Eq. (66), which is derived by solving the heat equation in Appendix A with λ already present in Eq. (A1) and in the boundary fluxes Eq. (A3). This is a consistency check rather than an independent derivation, and the paper says so. The nonlinear McLennan-Zubarev claim, Eqs. (122)-(123), is a formal consequence of choosing P(0)=P_lc and writing P(t)=P_lc exp[D(t)]; the load-bearing gap is the unproven assertion that Plc relaxes to Pst in a microscopic time. The paper explicitly flags this in Remark (6): 'Numerical study of the relaxation Plc → Pst should be informative.' This is an omitted proof or timescale assumption, not a circular reduction, and it should be weighed as a correctness risk rather than as circularity. No load-bearing self-citation chain or imported uniqueness theorem was found; self-citations such as Refs. [18] and [44] are contextual or provide auxiliary hydrodynamic results. Overall, the paper's central derivation retains independent content and the circularity is minor and localized.

Assumptions & free parameters 0 free parameters · 9 assumptions · 0 invented entities

The paper introduces no free parameters fitted to data. Its axioms are standard statistical mechanics, the specific Nosé-Hoover thermostat model, and the fast-thermostat and rapid local-equilibration assumptions that underpin the central derivations. No new physical entities are postulated.

assumptions (9)
  • standard math Liouville equation and phase-space distribution P(Γ,t) (Eqs. (27)-(28)).
    Foundation of the response derivation; assumed without proof.
  • domain assumption Nosé-Hoover thermostat equations of motion with constant τ_h (Eqs. (16)-(17)).
    The thermostat model is chosen; the paper argues results are independent of this choice on long times.
  • domain assumption Equilibrium distribution Pe(Γ) = (γ/2π) exp[βF − βH − Σ_K γ ζ_K^2/2] with γ = dM τ_h^2 (Eqs. (29)-(30)).
    Assumed stationary solution; needed for all equilibrium correlation functions.
  • ad hoc to paper Fast thermostat assumption: τ_h ≪ τ_m and J_K ≈ I_K (Eq. (34)).
    Load-bearing approximation used to replace thermostat heat flows by mechanical boundary heat flows; not rigorously derived.
  • domain assumption Linearized hydrodynamic equations with Fourier's law λ (Eq. (A1)) for the film interior.
    Used in Appendix A to evaluate time-correlation functions and the dissipation function; assumes the existence of λ.
  • domain assumption Piston effect: pressure homogenizes after sound traversal, leading to Eq. (A6).
    Standard for confined fluids; used to compute temperature relaxation and correlation integrals.
  • ad hoc to paper Rapid microscopic relaxation from the local-equilibrium distribution P_lc to the steady state P_st (Section IV E).
    Key assumption in the 'first principles' derivation of the McLennan-Zubarev distribution; no proof is given.
  • ad hoc to paper Linear profile δ\bar{T}(z) = δT_bot + T z approximates the transient temperature deviation (Eqs. (54)-(55)).
    Used to rewrite the dissipation function time derivative; exact only in steady state.
  • standard math Long-range correlations in the canonical ensemble via thermodynamic fluctuation theory (Appendix C).
    Standard result (Lebowitz-Percus) used to derive local-equilibrium response.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems." pith.science (2026). https://pith.science/paper/VDP5ODTZ

@misc{pith2026190807202,
  author       = {Pith},
  title        = {Pith review of: Theory of Applying Heat Flow from Thermostatted Boundary Walls: Dissipative and Local-Equilibrium Responses and Fluctuation Theorems},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VDP5ODTZ}},
  note         = {Machine review of arXiv:1908.07202}
}
abstract

We construct a microscopic theory of applying a heat flow from thermostatted boundary walls in the film geometry. We treat a classical one-component fluid, but our method is applicable to any fluids and solids. We express linear response of any variable ${\cal B}$ in terms of the time-correlation functions between $\cal B$ and the heat flows ${\cal J}_K$ from the thermostats to the particles. Furthermore, the surface variables ${\cal J}_K$ can be written in the form of space integrals of bulk quantities from the equations of motion. Owing to this surface-to-bulk relation, the steady-state response functions consist of dissipative and local-equilibrium parts, where the former gives rise to Fourier's law with Green's expression for the thermal conductivity. In the nonlinear regime, we derive the steady-state distribution in the phase space in the McLennan-Zubarev form from the first principles. Some fluctuation theorems are also presented.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

69 extracted references · 68 canonical work pages

  1. [1]

    Zwanzig, ''Time-correlation functions and transport coefficients in statistical mechanics,'' Annu

    R. Zwanzig, ''Time-correlation functions and transport coefficients in statistical mechanics,'' Annu. Rev. Phys. Chem. 16 , 67-101 (1965)

    work page 1965

  2. [2]

    Hansen and I

    J.-P. Hansen and I. R. Mcdonald, Theory of Simple Liquids (Academic, 2006)

    work page 2006

  3. [3]

    D. J. Evans and G. P. Morriss, Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)

    work page 1990

  4. [4]

    Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)

    A. Onuki, Phase Transition Dynamics (Cambridge University Press, Cambridge, 2002)

    2002

  5. [5]

    Green, ''Markoff random processes and the statistical mechanics of time-dpendent phenomena

    M.S. Green, ''Markoff random processes and the statistical mechanics of time-dpendent phenomena. II. Irreversible processes in fluids,'' J. Chem. Phys. 22 , 398-413 (1954)

    work page 1954

  6. [6]

    Kadanoff and P.C

    L.P. Kadanoff and P.C. Martin, ''Hydrodynamic Equations and Correlation Functions,'' Ann. of Phys. 24 , 419-469 (1963)

    work page 1963

  7. [7]

    Landau and E.M

    L.D. Landau and E.M. Lifshitz, Fluid Mechanics (Pergamon, New York, 1959)

    work page 1959

  8. [8]

    Onsager, ''Reciprocal relations in irreversible processes.I.,'' Phys

    L. Onsager, ''Reciprocal relations in irreversible processes.I.,'' Phys. Rev. 37 , 405-426 (1931)

    work page 1931

Show all 69 references
  1. [9]

    Zwanzig, ''Memory effects in irreversible thermodynamics,'' Phys

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

    1961

  2. [10]

    Mori, ''Transport, Collective Motion, and Brownian Motion,'' Progr

    H. Mori, ''Transport, Collective Motion, and Brownian Motion,'' Progr. Theoret. Phys. 33 , 423-455 (1965)

    1965

  3. [11]

    Kubo, ''The fluctuation-dissipation theorem,'' Rep

    R. Kubo, ''The fluctuation-dissipation theorem,'' Rep. Prog. Phys. 29 , 255-284 (1966)

    1966

  4. [12]

    Mori, ''Statistical-Mechanical Theory of Transport in Fluids,'' Phys

    H. Mori, ''Statistical-Mechanical Theory of Transport in Fluids,'' Phys. Rev. 112 , 1829-1842 (1958)

    1958

  5. [13]

    J. A. McLennan, ''Nonlinear Effects in Transport Theory,'' Phys. Fluids 4 , 1319-1324 (1961)

    1961

  6. [14]

    D. N. Zubarev, Dokl. Akad. Nauk. SSSR 140, 92-95 (1961) [''The Statistical Operator for Nonequilibrium Systems,''Sov. Phys.-Doklady 6, 776 (1962)]; ''The Method of the Non-Equilibrium Statistical Operator and its Applications. I,'' Fortschritte der Physik 18 , 125-147 (1970)

    1961

  7. [15]

    Kawasaki and J

    K. Kawasaki and J. D. Gunton, ''Theory of Nonlinear Transport Processes: Nonlinear Shear Viscosity and Normal Stress Effect,'' Phys. Rev., A 8 , 2048-2064 (1973)

    1973

  8. [16]

    Kubo, ''Statistical-mechanical theory of irreversible processes.I

    R. Kubo, ''Statistical-mechanical theory of irreversible processes.I. General theory and simple applications to magnetic and conduction problems,'' J. Phys. Soc. Jpn. 12 , 570-586 (1957)

    1957

  9. [17]

    Procaccia, D

    I. Procaccia, D. Ronis, M. A. Collins, J. Ross, and I. Oppenheim, ''Statistical mechanics of stationary states. I. Formal theory,'' Phys. Rev. A 19 , 1290-1306 (1979)

    1979

  10. [18]

    Onuki and T

    A. Onuki and T. Kawasaki, ''Theory of applying shear strains from boundary walls : linear response in glasses,'' J. Chem. Phys. 150 , 124504 (2019)

    2019

  11. [19]

    Petravic and P

    J. Petravic and P. Harrowell, ''Linear response theory for thermal conductivity and viscosity in terms of boundary fluctuations,'' Phys. Rev. E 71 , 061201 (2005); ''Equilibrium calculations of viscosity and thermal conductivity across a solid-liquid interface using boundary f...

    2005

  12. [20]

    Bonetto, J.L

    F. Bonetto, J.L. Lebowitz, L. Rey-Bellet, ''Fourierfs law: a challenge to theorists'', Mathematical Physics 2000, 128-150, (Imperial College Press, London, 2000)

    2000

  13. [21]

    Barrat and F

    J.-L. Barrat and F. Chiaruttini, ''Kapitza resistance at the liquid-solid interface,'' Mol. Phys. 101 , 1605-1610 (2003)

    2003

  14. [22]

    R sjorde, D

    A. R sjorde, D. W. Fossmo, D. Bedeaux, S. Kjelstrup, and B. Hafskjold, ''Non-equilibrium molecular dynamics calculation of heat conduction in liquid and through liquid-gas interface,'' J. Colloid and Interface Sci. 232 , 178-185 (2000)

    2000

  15. [23]

    Hamanaka, R

    T. Hamanaka, R. Yamamoto, and A. Onuki, ''Molecular dynamics simulation of heat conduction in near-critical fluids,'' Phys. Rev. E 71 , 011507 (2005)

    2005

  16. [24]

    E. S. Landry and A. J. H. McGaughey,

  17. [25]

    Lepri, R

    S. Lepri, R. Livi, and A. Politi, ''Energy transport in anharmonic lattices close to and far from equilibrium,'' Physica D 119 , 140-147 (1998)

    1998

  18. [26]

    Lepri, R

    S. Lepri, R. Livi, and A. Politi, ''Thermal conduction in classical low-dimensional lattices,'' Phys. Rep. 377 , 1-80 (2003)

    2003

  19. [27]

    M. M. Sano and K. Kitahara, ''Thermal conduction in a chain of colliding harmonic oscillators revisited,'' Phys. Rev. E 64 , 056111 (2001); K. Aoki and D. Kusnezov, ''Fermi-Pasta-Ulam b Model: Boundary Jumps, Fourier's Law, and Scaling,'' Phys. Rev. Lett. 86 , 4029 (2001)

    2001

  20. [28]

    Dhar, ''Heat transport in low-dimensional systems,'' Adv

    A. Dhar, ''Heat transport in low-dimensional systems,'' Adv. in Phys. 57 , 457-537 (2008)

    2008

  21. [29]

    D. J. Evans and D. J. Searles, ''Equilibrium microstates which generate second law violating steady states,'' Phys. Rev. E 50 , 1645 (1994); ''The Fluctuation Theorem,'' Adv. in Phys. 51 , 1529-15851 (2002)

    1994

  22. [30]

    Gallavotti and E

    G. Gallavotti and E. G. D. Cohen, ''Dynamical Ensembles in Stationary States,'' J. Stat. Phys. 80 , 931-970 (1995); ''Dynamical Ensembles in Nonequilibrium Statistical Mechanics,''Phys. Rev. Lett. 74 , 2694 (1995)

    1995

  23. [31]

    Jarzynski, ''Nonequilibrium equality for free energy differences,'' Phys.Rev

    C. Jarzynski, ''Nonequilibrium equality for free energy differences,'' Phys.Rev. Lett. 78 , 2690-93 (1997)

    1997

  24. [32]

    Jarzynski, ''Hamiltonian Derivation of a Detailed Fluctuation Theorem,'' J

    C. Jarzynski, ''Hamiltonian Derivation of a Detailed Fluctuation Theorem,'' J. Stat. Phys. 98 , 77-102 (2000)

    2000

  25. [33]

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

    1999

  26. [34]

    63 , 2361-2366 (2000)

    ''Path-ensemble averages in systems driven far from equilibrium,'' ibid. 63 , 2361-2366 (2000)

    2000

  27. [35]

    J. L. Lebowitz and H. Spohn, ''A Gallavotti-Cohen-Type Symmetry in the Large Deviation Functional for Stochastic Dynamics,'' J. Stat. Phys. 95 , 333-365 (1999)

    1999

  28. [36]

    Bustamante, J

    C. Bustamante, J. Liphardt, and F. Ritort, '' The nonequilibrium thermodynamics of small systems,'' Physics Today 58 , 7, 43-48 (2005)

    2005

  29. [37]

    D. J. Evans, D. J. Searles, and S. R. Williams, ''On the fluctuation theorem for the dissipation function and its connection with response theory, '' J. Chem. Phys. 128 , 014504 (2008)

    2008

  30. [38]

    Seifert, ''Stochastic thermodynamics, fluctuation theorems and molecular machines,'' Rep

    U. Seifert, ''Stochastic thermodynamics, fluctuation theorems and molecular machines,'' Rep. Prog. Phys. 75 , 126001 (2012)

    2012

  31. [39]

    D. J. Searles and D. J. Evans, ''Fluctuation Theorem for Heat Flow,'' Int. J. Thermophys. 22 , 123 (2001)

    2001

  32. [40]

    Jarzynski D

    C. Jarzynski D. K.W\' o jcik, ''Classical and Quantum Fluctuation Theorems for Heat Exchange,'' Phys. Rev. Lett. 92 , 230602 (2004)

    2004

  33. [41]

    S. R. Williams, D. J. Searles, and D. J. Evans, ''Nonequilibrium Free-Energy Relations for Thermal Changes,'' Phys. Rev. Lett. 100 , 250601 (2008)

    2008

  34. [42]

    T. S. Komatsu, N. Nakagawa, S. Sasa, and H. Tasaki, ''Entropy and Nonlinear Nonequilibrium Thermodynamic Relation for Heat Conducting Steady States'', J. Stat. Phys. 134 , 401-423 (2009); ''Exact Equalities and Thermodynamic Relations for Nonequilibrium Steady States,'' ibid. ...

    2009

  35. [43]

    D. J. Evans, D. J. Searles, and S. R. Williams, '' On the probability of violations of Fourier's law for heat flow in small systems observed for short times,'' J. Chem. Phys., 132 , 024501 (2010)

    2010

  36. [44]

    Kanazawa, T

    K. Kanazawa, T. Sagawa, and H. Hayakawa, ''Heat conduction induced by non-Gaussian athermal fluctuations,'' Phys. Rev. E 87 , 052124 (2013)

    2013

  37. [45]

    Nos\'e, ''A molecular dynamics method for simulations in the canonical ensemble,'' Mol

    S. Nos\'e, ''A molecular dynamics method for simulations in the canonical ensemble,'' Mol. Phys. 52 , 255-268 (1984); ''Constant temperature molecular dynamics methods,'' Progr. Theoret. Phys. (Kyoto), 103 , 1-46 (1991)

    1984

  38. [46]

    W. G. Hoover, ''Canonical dynamics: Equilibrium phase-space distributions,'' Phys. Rev. A 31 , 1695-1697 (1985)

    1985

  39. [47]

    Onuki and R

    A. Onuki and R. A. Ferrell, ''Adiabatic Heating Effect near the Gas-Liquid Critical Point,'' Physica A 164 , 245-264 (1990)

    1990

  40. [48]

    Garrabos, M

    Y. Garrabos, M. Bonetti, D. Beysens, F. Perrot, T. Fr o hlich, P. Carl e es, and B. Zappoli, ''Rlaxation of a supercritical fluid after a heat pulse in absence of gravity effects,'' Phys. Rev. E 57 , 5665 (1998)

    1998

  41. [49]

    Miura, S

    Y. Miura, S. Yoshihara, M. Ohnishi, K. Honda, M. Matsumoto, J. Kawai, M. Ishikawa, H. Kobayashi, and A. Onuki, ''High-speed observation of the piston effect near the gas-liquid critical point,'' Phys.Rev. E 74 , 010101(R) (2006)

    2006

  42. [50]

    Onuki, Thermoacoustic effects in supercritical fluids

    A. Onuki, Thermoacoustic effects in supercritical fluids

  43. [51]

    M. M. Mansour, J. W. Turner, and A. L. Garcia,

  44. [52]

    J. L. Lebowitz and J. K. Percus, ''Long-Range Correlations in a Closed System with Application to Nonuniform Fluids,'' Phys. Rev. 124 , 1673-1691 (1961)

    1961

  45. [53]

    J. L. Lebowitz, J. K. Percus, and L.Verlet, ''Ensemble dependence of fluctuations with application to machine computations,'' ibid. 153 , 250-254 (1967)

    1967

  46. [54]

    Shiba and A

    H. Shiba and A. Onuki, '' Plastic deformations in crystal, polycrystal, and glass in binary mixtures under shear: collective yielding, '' Phys. Rev. E 81 , 051501 (2010)

    2010

  47. [55]

    J. H. Irving and J. G. Kirkwood, ''The statistical mechanical theory of transport processes. IV. The equations of hydrodynamics.'' J. Chem. Phys. 18 , 817-829 (1949)

    1949

  48. [56]

    Puech, G

    L. Puech, G. Bonfait, and B. Castaing, ''Mobility of the 3He Solid-Liquid Interface: Experiment and Theory,'' J. Low Temp. Phys. 62 , 315-327 (1986)

    1986

  49. [57]

    Helfand, ''Transport coefficients from dissipation in a canonical ensemble,'' Phys

    E. Helfand, ''Transport coefficients from dissipation in a canonical ensemble,'' Phys. Rev. 119 , 1-9 (1960)

    1960

  50. [58]

    Viscardy, J

    S. Viscardy, J. Servantie, and P. Gaspard, ''Transport and Helfand moments in the Lennard-Jones fluid. II. Thermal conductivity,'' J. Chem. Phys. 126 , 184513 (2007)

    2007

  51. [59]

    W. Q. Hoover, A. J. C. Ladd, and B. Moran, ''High-Strain-Rate Plastic Flow Studied via Nonequilibrium Molecular Dynamics,'' Phys. Rev. Lett. 48 , 1818 (1982)

    1982

  52. [60]

    H. B. Callen, Thermodynamics (Wiley, New York,1960)

    1960

  53. [61]

    Landau and E.M

    L.D. Landau and E.M. Lifshitz, Statistical Physics (Pergamon, New York, 1964)

    1964

  54. [62]

    Suzuki, ''Irreversibility and entropy production in transpo

    M. Suzuki, ''Irreversibility and entropy production in transpo

  55. [63]

    S. K. Schnell, X. Liu, J.-M. Simon, A. Bardow, D. Bedeaux, T. J. H. Vlugt, and S. Kjelstrup, ''Calculating thermodynamic properties from fluctuations at small scales,'' J. Phys. Chem. B 115 , 10911-10918 (2011)

    2011

  56. [64]

    Cortes-Huerto, K

    R. Cortes-Huerto, K. Kremer, and R. Potestio, ''Communication: Kirkwood- Buff integrals in the thermodynamic limit from small sized molecular dynamics simulations,'' J. Chem. Phys. 145 , 141103 (2016)

    2016

  57. [65]

    B. M. Rogers, ''Extension of Kirkwood-Buff theory to the canonical ensemble, J. Chem. Phys. 148 , 054102 (2018)

    2018

  58. [66]

    Onuki, ''On fluctuations in space,'' J

    A. Onuki, ''On fluctuations in space,'' J. Stat. Phys. 18 , 475-499 (1978). See also Eq.(5.4.28) in Ref. [4]

    1978

  59. [67]

    Dorfman, T

    J.R. Dorfman, T. R. Kirkpatrick, and J. V. Sengers, ''Generic long-range correlations in molecular fluids,'' Ann. Rev. Phys. Chem. 45 , 213-239 (1994). references document

    1994

  60. [68]

    Onuki, ''Dynamic van der Waals theory,''

    A. Onuki, ''Dynamic van der Waals theory,''

  61. [69]

    T. R. Kirkpatrick, J. R. Dorfman, and J. V. Sengers, ''Work, work fluctuations, and the work distribution in a thermal nonequilibrium steady state,'' Phys.Rev. E 94 , 052128 (2016)

    2016

Pith tools

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