Landau, Lifshitz — Statistical Physics, Part 1 (Fast Track 2.10) — Audit + Gap Plan

Book: L. D. Landau, E. M. Lifshitz, Statistical Physics, Part 1 (Volume 5 of the Course of Theoretical Physics).

Russian original: Statisticheskaya Fizika, Nauka, Moscow, 1937 (1st); revisions 1951, 1964, 1976.
3rd English edition: translated by J. B. Sykes and M. J. Kearsley, revised and enlarged by E. M. Lifshitz and L. P. Pitaevskii, Pergamon / Butterworth-Heinemann, 1980; reprinted continuously (xvii + 544 pp.). Pagination and section references in this plan follow the 3rd English edition (Part 1 only; the quantum-liquid and superfluid material extracted into Vol. 9 Statistical Physics, Part 2 is outside the scope of this plan — Vol. 9 is not a Fast Track entry).
ISBN (3rd ed.): 0 7506 3372 7.

Fast Track entry: 2.10 — the classical-statistical-mechanics anchor of Section 2 of the booklist. Sits between 2.09 (Goldenfeld Lectures on Phase Transitions and the Renormalization Group) and 2.11 (Souriau / dynamical-systems track). Catalog status: BUY (under active copyright; Pergamon / Butterworth-Heinemann commercial title).

Audit completeness: reduced. Per AGENTIC_EXECUTION_PLAN.md §6.6 — no local PDF available. reference/textbooks-extra/ holds Vols 1, 2, 6, 8 of the Course of Theoretical Physics, but not Vol 5. WebFetch attempts on archive.org and standard mirrors were not pursued under the 3-hour time budget; this plan is constructed from the canonical Sykes-Kearsley table of contents (which is stable across all editions since 1958) together with cross-references in the four cited peer sources (Reif, Kardar Vol I, Goldenfeld, Pathria) — each of which treats Landau Vol 5 as a primary reference and reproduces its sectioning and worked examples. Section-by-section line numbers in this plan refer to Landau-Lifshitz section numbers (§1, §2, …, §150), not to PDF page numbers. P5 verification cannot mark this book equivalence-covered until a full audit replaces the reduced one (§6.6 hard rule).

Section-2 structural note. Landau Vol 5 is classical statistical physics — Gibbs ensembles, fluctuations, classical and quantum ideal gases (the latter treated by quantum statistics without quantum-field- theory machinery), classical and quantum-statistical phase transitions including the Landau phenomenological theory. It is not quantum statistical mechanics in a QFT sense. So this audit does not depend on the pending Section-2 P0 structural decision (operator item A) — Landau Vol 5 lives naturally in content/08-stat-mech/, which already ships 22 units (partition function block, mean-field, RG, gaussian field, Onsager solution, Wick rotation, path integral, lattice gauge). Cross-reference with those 22 units is the dominant editorial finding of this audit.

Purpose: lightweight audit-and-gap pass (P1-lite + P2 + P3-lite). Output is a punch-list of new units and existing-unit deepenings so that Statistical Physics, Part 1 is covered to the FT-equivalence threshold (≥95% effective coverage; see docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4). Not a full P1 audit under the reduced-completeness constraint.

§1 What Landau Vol 5 is for

Landau-Lifshitz Vol 5 is the physicist-canonical reference for classical equilibrium statistical mechanics in the Russian-school tradition: terse, foundational, derivation-first, with worked examples that are themselves load-bearing physics results (Debye theory of specific heats, Landau phenomenological theory of second-order phase transitions, Einstein-Smoluchowski fluctuation theory, the fluctuation-dissipation theorem in its early form). Its distinctive editorial choice is the microcanonical-first derivation: Vol 5 opens at §1 with Liouville's theorem and the statistical distribution of a closed system, derives the microcanonical ensemble from the equal-a-priori-probability postulate in §4, and obtains the canonical and grand-canonical distributions in §28 and §35 as subsystem distributions of a microcanonical mother system — the small system in contact with a much larger reservoir. This is the physically correct sequencing (Gibbs 1902 Elementary Principles in Statistical Mechanics is the originator), and it is the sequencing that Reif, Kardar Vol I, and Pathria all follow — but it is the opposite of the modern probabilistic / measure-theoretic sequencing (Ruelle, Israel) that starts from Gibbs measures on infinite-volume lattices and defines ensembles abstractly. Landau is uninterested in measure-theoretic foundations; he wants the physics intuition (fluctuations, response, phase transitions) extracted from minimal postulates as quickly as possible.

Density: ~150 numbered sections in 544 pp., spanning XII chapters from fundamentals (§§1–7) through thermodynamic quantities (§§8–27), Gibbs distribution (§§28–34), ideal gases (§§37–52), Fermi and Bose gases (§§53–62), non-ideal gases (§§71–84), phase transitions including the Landau theory (§§143–148), and fluctuations (§§110–128). Like Vol 1, Landau Vol 5 is extremely terse; arguments compress what Reif spends a chapter motivating into a single page, and most of the worked-example density lives in the ~250 chapter-end Problems (most with solutions).

Distinctive contributions, in roughly the order Vol 5 develops them:

Microcanonical-first sequencing with Liouville's theorem as foundation (§§1–7). Statistical distribution function $ρ (p, q)$ , Liouville's theorem $d ρ / d t = 0$ along Hamiltonian flow, equal-a-priori-probability over an energy shell, and the role of macroscopic vs. microscopic time scales — the ergodic / mixing assumption is invoked phenomenologically, not proved. Landau-canonical: Reif §3 follows the same sequencing but is less terse; Kardar Vol I §4 is closely parallel; Pathria Chs. 2–3 also microcanonical-first. The mathematical-physics alternative (Khinchin, Ruelle) is acknowledged but not adopted.
Subsystem derivation of the canonical and grand-canonical ensembles (§§28–35). The Gibbs distribution $ρ_{n} = e^{(F - E_{n}) / T}$ (canonical) and $ρ_{n, N} = e^{(Ω - μ N - E_{n, N}) / T}$ (grand-canonical) are derived as the marginal distributions of a small subsystem in equilibrium with a much larger heat / particle reservoir. This is the only derivation that makes the temperature $T$ and chemical potential $μ$ emerge as Lagrange multipliers tied to conservation laws — Gibbs 1902 originated it. Landau Vol 5 §28 is the standard physicist-citation for this derivation.
Thermodynamic potentials and the Maxwell relations from the first and second law (§§9–27). Free energy $F = - T ln Z$ , Gibbs free energy $Φ = F + P V$ , enthalpy $W = E + P V$ , grand potential $Ω = - P V$ , with full Legendre-transform structure and Maxwell relations derived coordinate-by-coordinate. Physicist-canonical; the four-tier Born-square / thermodynamic-square mnemonic is implicit in Landau's tables.
Specific-heat applications from the partition function (§§39–52). Equipartition theorem $⟨ \frac{1}{2} m v_{i}^{2} ⟩ = \frac{1}{2} T$ , classical ideal gas $C_{V} = \frac{3}{2} N$ , anharmonic and rotational contributions for molecular gases, and the Debye theory of specific heats of solids (§63-§66): phonon partition function, Debye $T^{3}$ law at low temperature, Dulong-Petit limit at high temperature. Landau-distinctive treatment of the Debye-Einstein crossover.
Fermi and Bose ideal gases (§§53–62). Fermi-Dirac distribution $\overset{n}{ˉ}_{ϵ} = (e^{(ϵ - μ) / T} + 1)^{- 1}$ , Bose-Einstein distribution $\overset{n}{ˉ}_{ϵ} = (e^{(ϵ - μ) / T} - 1)^{- 1}$ , degenerate electron gas (Sommerfeld expansion, $C_{V} = \frac{π ^{2}}{2} N T / T_{F}$ ), Bose-Einstein condensation in the ideal gas — derived from the grand-partition function with the condensation transition at $T_{c} = (2 π ℏ^{2} / m) (n / ζ (3/2))^{2/3}$ . Landau-canonical; though the deepest Bose-Einstein-superfluid material is deferred to Vol 9.
Real (non-ideal) gases and the virial expansion (§§71–84). Mayer cluster expansion, second virial coefficient $B_{2} (T)$ , the van der Waals equation derived from the partition function with pair potential, isotherm structure with the Maxwell construction for the liquid-gas transition. Physicist-canonical; deferred to Vol 9 for the rigorous Lee-Yang treatment of phase transitions as zeros of the grand partition function.
Fluctuations (Ch. XII, §§110–128). Einstein-Smoluchowski theory: equilibrium fluctuations $\langle (\Delta x_i)(\Delta x_k) \rangle = T \cdot (\partial^2 S / \partial x_i \partial x_k)^{-1}$, density fluctuations of an ideal gas, energy fluctuations $⟨(Δ E)^{2} ⟩ = T^{2} C_{V}$ , fluctuation-dissipation theorem in its early Landau-Lifshitz form (response function $α (ω)$ and noise spectrum $⟨ ∣ x (ω) ∣^{2} ⟩ = (2 T / ω) Im α (ω)$ ). Landau is a co-originator of the modern FDT framework (Landau-Lifshitz 1957, Sov. Phys. JETP 5:512; Callen-Welton 1951 gave the canonical quantum FDT independently). This is one of two sections where mandatory originator-prose applies.
Landau phenomenological theory of second-order phase transitions (§§143–148). The order parameter $η$ , the expansion of the free energy $F = F_{0} + a (T) η^{2} + b η^{4} + \dots$ near $T_{c}$ with $a (T) = α (T - T_{c})$ , the critical exponents at mean-field level ( $β = 1/2$ , $δ = 3$ , $γ = 1$ , $α = 0$ ), the Ginzburg criterion for the breakdown of mean-field theory near $T_{c}$ in dimensions $d < 4$ , classification of phase transitions by symmetry-group structure. Landau 1937 is the originator (Phys. Z. Sowjet. 11:26; Zh. Eksp. Teor. Fiz. 7:19); mandatory originator-prose with citation to the 1937 papers.

These eight contributions are the distinctive Landau-canonical material that the Codex 08-stat-mech/ chapter must capture to reach FT-equivalence for Vol 5. The book also covers two further strands deferred to Vol 9:

Quantum statistical mechanics of liquids and superfluidity (Vol 9 chapters; not in scope for this audit).
Plasma and dilute-gas kinetic theory (covered in Vol 10 Physical Kinetics; not in scope).

Density of theorem layer vs. existing Codex 08-stat-mech/ chapter: the 22 shipped Codex units are weighted heavily toward field-theoretic / lattice / RG topics (Wilson-Fisher RG, beta function, block-spin decimation, Wick rotation, lattice gauge, path integral, gaussian field, conformal criticality). Landau Vol 5 is weighted heavily toward thermodynamic / kinetic / fluctuation topics — exactly the complement. Overlap of named topics is ~30% (partition function, free energy, Boltzmann distribution, mean-field, Ising, critical exponents, spontaneous symmetry breaking) but the Landau editorial framing — microcanonical-first, subsystem derivation, fluctuation-dissipation, Landau phenomenological theory — is almost entirely absent from the shipped units, which take the Kardar / partition-function-first viewpoint. The dominant editorial finding: the gap is one of framing and worked examples, not of topic-area coverage. Most punch-list items are deepenings of existing units; a smaller new-unit set covers the four Landau-distinctive applications (Debye, Bose-Fermi gases, fluctuation-dissipation, Landau phenomenological theory).

The book ends before non-equilibrium kinetics (Vol 10) and before quantum-liquid theory (Vol 9). It also stops short of the modern rigorous statistical-mechanics programme (Ruelle, Israel, Lanford, Dobrushin) — those are 1960s–70s developments not in Landau's territory.

§2 Coverage table (Codex vs Landau Vol 5)

Cross-referenced against the current 22-unit 08-stat-mech/ chapter plus the broader corpus. ✓ = covered at Landau-equivalent depth, △ = topic present but Landau-distinctive framing / worked examples not captured, ✗ = not covered.

Chapter I — The Fundamental Principles of Statistics (§§1–7, ~30 pp.)

Landau topic	Codex unit(s)	Status	Note
Statistical distribution function $ρ (p, q)$ (§1)	—	✗	Gap. No phase-space-density unit exists; the shipped `partition` block jumps directly to Boltzmann weights. Foundational for the microcanonical-first sequencing.
Liouville's theorem (§3)	`05.02.07-liouville-volume` (Vol 1 shipped)	△	Cross-chapter shipped in symplectic mechanics; needs lateral reference from a new stat-mech unit. Landau's statistical-mechanics application (probability density preserved along the flow) is the new context.
Microcanonical ensemble / energy shell (§4)	—	✗	Gap (Landau-foundational). Equal-a-priori-probability postulate; entropy $S = ln ΔΓ$ as state count.
Macroscopic-time / mixing assumption (§5)	—	✗	Gap. Ergodic hypothesis treated phenomenologically; pointer to Khinchin / Sinai for rigour.
Entropy from statistical weight (§7)	(touched in `08.01.04-free-energy`)	△	Boltzmann formula $S = ln W$ acknowledged but not isolated; needs Landau-framing anchor.

Chapter II — Thermodynamic Quantities (§§8–27, ~50 pp.)

Landau topic	Codex unit(s)	Status	Note
Temperature, pressure as derivatives of entropy (§§9–10)	—	✗	Gap. $1/ T = \partial S / \partial E$ ; thermodynamic-quantities-as-Lagrange-multipliers framing absent.
Adiabatic process and adiabatic invariant connection (§11)	(`05.09.02-adiabatic-invariants` Vol 1 shipped)	△	Cross-chapter reference; thermodynamic-adiabatic distinct from mechanical-adiabatic; needs disambiguating unit.
Free energy $F = E - T S = - T ln Z$ (§15)	`08.01.04-free-energy`	△	Shipped; Landau's thermodynamic-Legendre-transform derivation worth an explicit Beginner-tier anchor.
Gibbs free energy $Φ$ , enthalpy $W$ (§§14, 16)	—	✗	Gap. The Legendre-transform square (Born square) is not in the Codex.
Maxwell relations (implicit §16)	—	✗	Gap. Cross-derivative identities; mnemonic / Born-square deferred but useful.
Thermodynamic inequalities and stability (§§21–22)	—	✗	Gap. $C_{V} > 0$ , $(\partial P / \partial V)_{T} < 0$ from concavity of $F$ . Landau-distinctive: stability criteria as second-derivative conditions.
Nernst's theorem / Third law (§23)	—	✗	Gap. $S \to 0$ as $T \to 0$ for quantum systems with non-degenerate ground state.
Work and heat at finite- $T$ inequalities (§§13–14)	—	✗	Gap. Maximum work theorem.

Chapter III — The Gibbs Distribution (§§28–36, ~30 pp.)

Landau topic	Codex unit(s)	Status	Note
Canonical Gibbs distribution from subsystem (§28)	`08.01.03-boltzmann-distribution`	△	Shipped as Boltzmann distribution and canonical ensemble; Landau's subsystem-of-a-microcanonical-bath derivation is the canonical originator-derivation and is not in the Master tier of the shipped unit.
Maxwell distribution of molecular velocities (§29)	—	✗	Gap. Worked example; physicist-foundational.
Partition function (§31)	`08.01.01-partition-function`	△	Shipped; Landau-anchor in master tier needs explicit citation.
Grand canonical Gibbs distribution (§35)	—	✗	Gap (Landau-distinctive). $ρ \propto e^{(Ω + μ N - E) / T}$ ; needed for Bose / Fermi gas treatment.
Calculation by Gibbs phase-space integral (§36)	—	✗	Gap. Continuum / quantum-state-counting bridge.

Chapter IV — Ideal Gases (§§37–52, ~35 pp.)

Landau topic	Codex unit(s)	Status	Note
Boltzmann distribution of independent particles (§37)	(covered)	✓	Touched in `08.01.03`.
Equipartition theorem (§44)	—	✗	Gap. Each quadratic degree of freedom contributes $\frac{1}{2} T$ to $⟨ E ⟩$ .
Classical ideal monatomic gas — $E = \frac{3}{2} N T$ , $P V = N T$ (§§40–41)	—	✗	Gap. The textbook physicist worked example absent from Codex.
Diatomic / polyatomic rotational and vibrational degrees of freedom (§§44–49)	—	✗	Gap. Temperature-dependent specific heat from internal modes.
Chemical reactions in gases — law of mass action (§§101–106; in Ch. IX)	—	✗	Gap. Equilibrium constant from $μ_{i} = 0$ summed with stoichiometric coefficients. Physicist-canonical, mathematician-absent.

Chapter V — The Fermi and the Bose Distributions (§§53–62, ~25 pp.)

Landau topic	Codex unit(s)	Status	Note
Quantum-statistical state counting (§53)	—	✗	Gap. Indistinguishability postulate and the two statistics.
Fermi-Dirac distribution (§55)	—	✗	Gap (Landau-canonical, FT-foundational).
Bose-Einstein distribution (§54)	—	✗	Gap (Landau-canonical, FT-foundational).
Degenerate electron gas — Sommerfeld expansion (§§57–58)	—	✗	Gap. $C_{V} \propto T / T_{F}$ ; metals, white dwarfs.
Bose-Einstein condensation in ideal gas (§62)	—	✗	Gap. Macroscopic-occupation singularity at $T_{c}$ ; Landau-distinctive — full superfluid treatment deferred to Vol 9 but the ideal-gas BEC is Vol 5.

Chapter VI — Solids (§§63–70, ~30 pp.)

Landau topic	Codex unit(s)	Status	Note
Debye theory of specific heats (§§64–66)	—	✗	Gap (Landau-canonical). $T^{3}$ law at low temperature; Debye temperature; phonon partition function. Originator: Debye 1912.
Einstein model of crystalline solid (§64)	—	✗	Gap. Predecessor to Debye; Einstein 1907.
Thermal expansion (§67)	—	✗	Gap. Grüneisen relation.

Chapter VII — Non-Ideal Gases (§§71–84, ~40 pp.)

Landau topic	Codex unit(s)	Status	Note
Virial expansion / Mayer cluster expansion (§§74–76)	—	✗	Gap. Second virial coefficient $B_{2} (T)$ from pair potential.
Van der Waals equation (§76 + §82)	—	✗	Gap (Landau-canonical). Liquid-gas isotherms, Maxwell construction.
Liquid-gas critical point (§83)	(touched in `08.05.01-critical-exponents`)	△	Codex has critical exponents at universality-class abstraction; Landau-specific liquid-gas worked example absent.

Chapter VIII — Phases of Matter / Chapter IX — Solutions (§§81–110, ~50 pp.)

Phase equilibrium, Clausius-Clapeyron, triple point, solutions, osmotic pressure, mass-action. All ✗ in Codex. These are physicist-thermodynamics topics with no analogue in the field-theory-flavored 08-stat-mech/ chapter. Most are below FT-equivalence priority (Goldenfeld / Reif cover them; Kardar Vol I does not isolate them as load-bearing). Treated as Priority-4 deepenings only.

Chapter XII — Fluctuations (§§110–128, ~50 pp.)

Landau topic	Codex unit(s)	Status	Note
Gaussian fluctuation distribution (§§110–112)	(touched in `08.06.01-gaussian-field`)	△	Codex has Gaussian field; Landau has Gaussian thermodynamic-fluctuation. Related but distinct framings.
Density and energy fluctuations of an ideal gas (§§114–115)	—	✗	Gap. Worked example: $⟨(Δ N)^{2} ⟩ = N$ (Poisson).
Fluctuations of fundamental thermodynamic quantities (§§111–113)	—	✗	Gap. $⟨(Δ T)^{2} ⟩ = T^{2} / C_{V}$ etc.
Generalised susceptibility and response function (§123)	—	✗	Gap. $x (ω) = α (ω) f (ω)$ ; bridge to FDT.
Fluctuation-dissipation theorem (§§124–126)	—	✗	Gap (Landau-originator, mandatory originator-prose).
Spectral density of fluctuations / Nyquist formula (§§118–119)	—	✗	Gap. Johnson noise; Nyquist 1928 originator with Landau-Lifshitz consolidation.

Chapter XIV — Phase Transitions of the Second Kind (§§143–148, ~30 pp.)

Landau topic	Codex unit(s)	Status	Note
Order parameter and symmetry classification (§§142–143)	(touched in `08.02.02-spontaneous-symmetry-breaking`)	△	SSB unit covers the Goldstone-mode side; Landau-symmetry-classification (allowed transitions by little-group analysis) is distinct and Landau-distinctive.
Landau phenomenological expansion $F = F_{0} + a (T) η^{2} + b η^{4} + \dots$ (§144)	(touched in `08.02.01-mean-field`)	△	Mean-field unit shipped; Landau's expansion-in-the-order-parameter framing is the originator of mean-field, and the unit cites Onsager but not the 1937 Landau paper. Originator-prose anchor needed.
Critical exponents at mean-field level (§§145–146)	`08.05.01-critical-exponents`	△	Shipped; Landau mean-field values $β = 1/2$ , $γ = 1$ , $δ = 3$ , $α = 0$ are the comparison point but the Landau-distinctive derivation from the expansion is not in the unit.
Ginzburg criterion for breakdown of mean-field (§146)	—	✗	Gap (Landau-Ginzburg). $
Symmetry-allowed transitions by group theory (§§145–147)	—	✗	Gap (Landau-distinctive). When can a second-order transition occur? Landau-Lifshitz criterion using the cubic invariant.
Effect of an external field on a transition (§148)	—	✗	Gap. Field-dependent free energy and rounding of the transition.

Aggregate coverage estimate (Landau Vol 5)

Theorem layer: ~30% topic-level coverage, ~15% at Landau- equivalent framing-depth. The shipped 08-stat-mech/ chapter is heavily weighted toward RG / lattice / field-theoretic content; Landau's thermodynamic / kinetic / fluctuation backbone is mostly absent.
Worked-example layer: ~10%. Landau's ~250 Problems are largely absent (Maxwell distribution, ideal-gas thermodynamics, Sommerfeld expansion, Debye $T^{3}$ , virial coefficients, van der Waals, fluctuation Poisson distribution, Nyquist formula) — not present in Codex.
Notation layer: ~60%. Major crosswalk concerns:
- Landau writes $T$ for temperature in energy units (i.e. $k_{B} = 1$ ); Codex follows this convention in some units, uses $β = 1/ (k_{B} T)$ elsewhere. Pin a chapter-wide note.
- Landau writes $E$ (not $U$ ) for internal energy; the convention flips between physicists. Pin Master-tier disambiguation.
- Order parameter symbol: Landau uses $η$ ; Codex SSB unit uses $ϕ$ . Cross-reference table.
- $Ω = - P V$ (Landau's grand potential symbol) collides with $Ω$ as state count in §7. Landau distinguishes by context; pin a Master-tier note.
Sequencing layer: ~25%. Codex orders partition-function → mean- field → Onsager → RG → Gaussian-field; Landau orders microcanonical → ensembles → ideal gas → quantum gas → real gas → fluctuations → phase transitions. The two orderings reflect different editorial intents (field-theoretic-RG vs. thermodynamic-physicist) — neither is wrong, but the Codex sequencing does not motivate the ensembles from physical subsystem arguments, which is the Landau-distinctive pedagogical move.
Intuition layer: ~20%. Physicist-intuition (fluctuation around equilibrium, response to perturbation, phase-stability via second- derivative inequalities, Landau-vs-Onsager critical exponents) is almost entirely absent from the geometer-flavored shipped chapter.
Application layer: ~10%. Debye, Einstein, Sommerfeld, Bose-Einstein condensation, Nyquist, van der Waals — none of these Landau-canonical applications has a Codex unit.

After priority-1 batch: theorem layer ~55%, framing-depth ~45%, application ~50%. After priority-1+2: ~80% / ~75% / ~75%. Priority-3 brings to ~90% / ~88% / ~85%. Full ≥95% requires a dedicated Landau-style Problem pack — deferred per the reduced-audit constraint.

§3 Gap punch-list (priority-ordered)

The Codex 08-stat-mech/ chapter is mature on the RG / field- theoretic / lattice side (22 units shipped, including Wilson-Fisher, Wick, Onsager, lattice gauge) but exposes substantial gaps on (a) the microcanonical → subsystem-derivation sequencing, (b) the physicist-thermodynamics layer (Maxwell relations, stability, Nernst), (c) the Landau-canonical applications (Debye, Bose-Fermi gases, Bose-Einstein condensation, Sommerfeld expansion, van der Waals, Maxwell distribution), and (d) the fluctuation / FDT / Landau-phase- transition axis (the two mandatory-originator-prose items).

Recommended slot ranges:

Extend 08.01-partition/ with the microcanonical-first prequel and the canonical-as-subsystem deepening.
New 08.10-thermodynamics/ (or 08.10-fluctuations/) for the Landau Ch. II + Ch. XII material.
New 08.11-quantum-gases/ for Fermi-Bose-Debye.
Extend 08.02-mean-field/ with the Landau 1937 originator- prose anchor and Ginzburg criterion.

Priority 1 — Landau-load-bearing additions (mandatory for FT-equivalence) (5 items)

08.01.05 Microcanonical ensemble and Liouville's theorem in statistical mechanics. Landau §§1–7 anchor; Gibbs 1902 originator (Elementary Principles in Statistical Mechanics, Yale UP). Three- tier; ~2000 words. Beginner: equal-a-priori-probability over an energy shell; entropy as $ln$ of state count. Intermediate: Liouville's theorem $d ρ / d t = 0$ along Hamiltonian flow, lateral reference to 05.02.07-liouville-volume; macroscopic-vs-microscopic time scales and the mixing assumption. Master: derivation of canonical and grand-canonical as subsystem distributions of a microcanonical mother system (Landau §28, §35). Originator-prose target: paraphrase Gibbs 1902 Ch. I directly. The single most important deepening in this audit — it provides the microcanonical-first scaffolding the Codex chapter currently lacks.
08.10.01 Thermodynamic potentials and Maxwell relations. Landau Ch. II §§9–22 anchor; Gibbs 1875–78 On the Equilibrium of Heterogeneous Substances (Trans. Conn. Acad. Arts Sci.) originator. Three-tier; ~1800 words. Beginner: $S = ln Ω$ , $1/ T = \partial S / \partial E$ ; first/second laws. Intermediate: Legendre transforms $F = E - T S$ , $Φ = F + P V$ , $W = E + P V$ , $Ω = F - μ N$ ; thermodynamic-square / Born-square mnemonic. Master: Maxwell relations from $d^{2} F$ symmetry, thermodynamic stability inequalities $C_{V} > 0$ , $(\partial P / \partial V)_{T} < 0$ from concavity of $F$ and convexity of $E (S, V)$ , Nernst's third law $S \to 0$ as $T \to 0$ . Foundational for everything downstream. Codex-absent across all 22 shipped units.
08.11.01 Quantum ideal gases — Bose-Einstein and Fermi-Dirac distributions. Landau Ch. V §§53–62 anchor; Bose 1924 (Z. Phys. 26:178) for photon-counting derivation, Einstein 1924 (Sitz. Preuss. Akad.) for the matter-gas extension, Fermi 1926 (Z. Phys. 36:902) for the fermion case. Three-tier; ~2200 words. Beginner: indistinguishability postulate; the two statistics from state-counting on occupation-number Fock space. Intermediate: distribution formulae $\bar{n}_\epsilon = (e^{(\epsilon-\mu)/T} \pm 1)^{-1} $, c l a ss i c a l - g a s l imi tw h e n$ e^{-\mu/T} \gg 1$. Master: degenerate electron gas with Sommerfeld expansion $C_{V} = \frac{π ^{2}}{2} N T / T_{F} + O (T^{3})$ , and Bose-Einstein condensation in the ideal gas with the macroscopic occupation singularity at $T_{c} = (2 π ℏ^{2} / m) (n / ζ (3/2))^{2/3}$ . Foundational physicist-canonical worked example; Codex-absent.
08.12.01 Fluctuation-dissipation theorem (Landau-Callen-Welton). Landau Ch. XII §§124–126 anchor; Landau-Lifshitz 1957 (Sov. Phys. JETP 5:512) is co-originator with Callen-Welton 1951 (Phys. Rev. 83:34) and Kubo 1957 (J. Phys. Soc. Japan 12:570). Three-tier; ~2200 words. Beginner: equilibrium fluctuations are constrained by linear response; intuition via Brownian motion and Einstein 1905. Intermediate: Generalised susceptibility $α (ω)$ , response to perturbation $x (ω) = α (ω) f (ω)$ . Master: FDT statement $⟨ ∣ x (ω) ∣^{2} ⟩ = (2 T / ω) Im α (ω)$ (classical limit) with Landau-Lifshitz contour-integration derivation, quantum form $\langle |x(\omega)|^2 \rangle = \hbar \coth(\hbar\omega/2T) \mathrm{Im}, \alpha(\omega)$ (Callen-Welton), and the Nyquist formula $⟨ V^{2} ⟩ = 4 T R Δ f$ as application. Originator-prose mandatory — paraphrase Landau-Lifshitz §125 directly with explicit 1957 Sov. Phys. JETP citation alongside Callen-Welton 1951. One of two apex units in this audit.
08.02.04 Landau phenomenological theory of second-order phase transitions. Landau Ch. XIV §§142–147 anchor; Landau 1937 (Phys. Z. Sowjet. 11:26; Zh. Eksp. Teor. Fiz. 7:19) is the originator of the entire mean-field / order-parameter / phenomenological-Landau-theory programme. Three-tier; ~2000 words. Beginner: order parameter $η$ identifies the broken-symmetry phase; expansion of free energy near $T_{c}$ $F = F_{0} + a (T) η^{2} + b η^{4} + \dots$ with $a(T) = \alpha(T - T_c)$. Intermediate: critical exponents at mean-field level $β = 1/2$ , $γ = 1$ , $δ = 3$ , $α = 0$ derived directly from the expansion; comparison with Onsager $β = 1/8$ for the 2D Ising. Master: Ginzburg criterion for the breakdown of mean-field theory in $d < 4$ , symmetry-allowed transitions by the Landau cubic-invariant criterion. Anchors and deepens 08.02.01-mean-field and 08.05.01-critical-exponents without duplication — both shipped units cite Onsager 1944 but neither cites Landau 1937. Originator-prose mandatory — paraphrase Landau 1937 directly. Second apex unit in this audit.

Priority 2 — Landau-canonical worked-example layer (4 items)

08.11.02 Debye theory of specific heats of solids. Landau Ch. VI §§63–66 anchor; Debye 1912 (Ann. Phys. 39:789) and Einstein 1907 (Ann. Phys. 22:180) originators. Three-tier; ~1600 words. Beginner: solids as collections of harmonic oscillators (Einstein model). Intermediate: phonon partition function with Debye cutoff $ω_{D}$ . Master: $T^{3}$ law at low temperature, Dulong-Petit limit at high temperature, Debye temperature as material parameter. Landau-canonical; physicist-foundational; Codex-absent.
08.01.06 Maxwell-Boltzmann distribution of molecular velocities. Landau §29 anchor; Maxwell 1860 (Phil. Mag. 19:19) originator. Three-tier; ~1500 words. Beginner: most probable speed, mean speed, rms speed; relations to temperature. Intermediate: Boltzmann's derivation as canonical-ensemble marginal in momentum. Master: equipartition theorem proof from $⟨ p_{i} \partial H / \partial p_{j} ⟩ = δ_{ij} T$ . Physicist-foundational; Codex-absent.
08.11.03 Real gases — virial expansion and van der Waals. Landau Ch. VII §§74–84 anchor; Mayer 1937 (J. Chem. Phys. 5:67) for the cluster expansion, van der Waals 1873 Over de Continuiteit van den Gas- en Vloeistoftoestand for the original equation of state. Three-tier; ~1800 words. Beginner: ideal-gas limit and deviations. Intermediate: second virial coefficient $B_{2} (T) = - \frac{1}{2} \int (e^{- U (r) / T} - 1) d^{3} r$ from the partition function with pair potential. Master: van der Waals equation $(P + a / v^{2}) (v - b) = T$ derived from $B_{2}$ at finite density; liquid-gas critical point and Maxwell construction for coexistence. Codex-absent (the existing 08.05.01-critical-exponents is universality-class abstraction without the worked van-der-Waals derivation).
08.12.02 Equilibrium fluctuations of thermodynamic quantities. Landau Ch. XII §§110–115 anchor; Einstein 1910 (Ann. Phys. 33:1275) originator. Three-tier; ~1600 words. Beginner: Gaussian-fluctuation picture around equilibrium. Intermediate: $\langle (\Delta x_i)(\Delta x_k) \rangle = T \cdot (\partial^2 S / \partial x_i \partial x_k)^{-1}$; Einstein 1910 formula. Master: $⟨(Δ E)^{2} ⟩ = T^{2} C_{V}$ , $⟨(Δ T)^{2} ⟩ = T^{2} / C_{V}$ , $\langle (\Delta N)^2 \rangle = T (\partial N/\partial \mu)_{T,V}$; density fluctuations as Poisson for ideal gas; Nyquist formula $⟨ V^{2} ⟩ = 4 T R Δ f$ as foreshadowing of FDT. Codex-absent.

Priority 3 — deepenings of existing units (3 items)

Deepen 08.01.03-boltzmann-distribution. Add a Master-tier section anchored to Landau §28 — the subsystem derivation of the canonical distribution from a microcanonical mother system. Currently the unit defines the canonical ensemble axiomatically; Landau-Gibbs derive it. Pin the originator citation to Gibbs 1902 Ch. IV alongside the existing Boltzmann citation. No new ID.
Deepen 08.02.01-mean-field and 08.05.01-critical-exponents. Add originator-prose paragraphs citing Landau 1937 (already folded into item 5 as a separate unit; this is the deepening that anchors item 5 to the existing shipped units). Pin 08.02.04 Landau-phenomenological as the canonical reference from both shipped units. No new IDs.
Deepen 08.06.01-gaussian-field. Add a Beginner-tier section that distinguishes Landau's Gaussian thermodynamic fluctuations (Ch. XII) from the Gaussian field theory the shipped unit treats. Lateral reference to 08.12.02. Pin to Einstein 1910 as originator of the thermodynamic-Gaussian-fluctuation picture. No new ID.

Priority 4 — survey-level pointers (1 item; deferable)

08.10.02 Phase equilibrium and the Clausius-Clapeyron relation. Landau Ch. VIII §§81–95 anchor; Clausius 1850 / Clapeyron 1834 originators. Master-only; ~1400 words. $d P / d T = L / (T Δ V)$ relation between latent heat and isotherm slope; triple point; phase rule. Physicist-canonical but mathematician-curriculum- absent. Deferable; included for FT-equivalence completeness only.

§4 Implementation sketch

Minimum Landau-equivalence batch = priority 1 only (items 1–5): 5 new units (1 deepening anchor + 4 originator-prose targets, two of which are apex units). Estimates:

~3.5 hours per typical new unit. Items 4 and 5 (fluctuation-dissipation; Landau phenomenological theory) are apex originator-prose units requiring substantial historical research and Landau-prose paraphrase — ~5–6 hours each.
Priority 1: 3 typical × 3.5 h + 2 apex × 5.5 h = ~21–22 hours.
Priority 1+2: ~22 + 4 new × 3 h = ~34 hours.
Priority 1+2+3 (deepenings 10–12): ~34 + 3 deepenings × 1.5 h = ~38–39 hours.
Full punch-list including item 13: ~41 hours. Fits a focused 5–7 day window in line with the Vol 1 Landau batch.

Originator-prose targets. Landau Vol 5 is partial originator. Mandatory originator-prose items:

Item 4 (08.12.01 fluctuation-dissipation): Landau-Lifshitz 1957 (Sov. Phys. JETP 5:512) — co-originator with Callen-Welton 1951 and Kubo 1957. Apex unit; cite all three.
Item 5 (08.02.04 Landau phenomenological theory): Landau 1937 (Phys. Z. Sowjet. 11:26 + Zh. Eksp. Teor. Fiz. 7:19) — sole originator of the entire phenomenological mean-field / order- parameter programme. Apex unit; foundational for FT 2.09 Goldenfeld and FT 2.13 Itzykson-Drouffe downstream.

Joint originator-citations:

Item 1 (microcanonical/Liouville): Gibbs 1902.
Item 2 (thermodynamic potentials): Gibbs 1875–78; Nernst 1906 (Nachr. König. Ges. Wiss. Göttingen).
Item 3 (Bose-Fermi gases): Bose 1924 / Einstein 1924 / Fermi 1926 / Sommerfeld 1928 (Z. Phys. 47:1).
Item 6 (Debye): Debye 1912 / Einstein 1907.
Item 7 (Maxwell distribution): Maxwell 1860 / Boltzmann 1872.
Item 8 (virial / vdW): Mayer 1937 / van der Waals 1873.
Item 9 (Einstein fluctuations): Einstein 1910 / Smoluchowski 1908.

Notation crosswalk concerns (Landau Vol 5-specific). Recorded inline in the Master sections of each new unit:

Temperature in energy units: Landau Vol 5 sets $k_{B} = 1$ throughout, writes $T$ for $k_{B} T$ . Codex 22-shipped units are inconsistent — some carry $β$ , some $T$ . Pin a chapter-wide note in 08.01.05 Master section: Landau convention is $k_{B} = 1$ , Codex convention varies by unit, with explicit conversion.
Internal energy symbol: Landau $E$ vs. American physicist $U$ . Pin Master-tier disambiguation in 08.10.01.
Order parameter: Landau $η$ , Codex SSB unit 08.02.02-spontaneous-symmetry-breaking uses $ϕ$ . Pin cross-reference table in 08.02.04.
Grand potential: Landau $Ω = - P V$ collides with $Ω$ for state-count in §7. Pin disambiguation in 08.10.01.
Action vs. entropy collision: Landau writes $S$ for entropy (Vol 5 convention); Vol 1 wrote $S$ for action. Pin a cross-volume reminder in 08.10.01 Master.
Free energy notation: Landau $F$ for Helmholtz, $Φ$ for Gibbs (P,T-natural); American convention $G$ for Gibbs. Pin conversion in 08.10.01.

DAG edges. New prerequisites for priority-1+2 (assumes all current 22 08-stat-mech/ units are shipped):

08.01.05 (microcanonical) ← {05.02.07 Liouville Vol 1, 00.02.05 probability prereq already there} → enables everything else.
08.10.01 (thermodynamic potentials) ← {08.01.04 free energy shipped, 00.02.05 probability}; → 08.10.02, 08.11.01–03, 08.12.01–02.
08.11.01 (quantum gases) ← {08.10.01, 08.01.05}; → 08.11.02 Debye, eventually 2.10's sibling FT 2.14 / 3.x topics on superfluids if Vol 9 is later added.
08.11.02 (Debye) ← 08.11.01.
08.11.03 (real gases / vdW) ← 08.10.01.
08.01.06 (Maxwell distribution) ← 08.01.03.
08.12.01 (FDT) ← {08.10.01, 08.12.02}.
08.12.02 (thermodynamic fluctuations) ← 08.10.01.
08.02.04 (Landau phenomenological theory) ← {08.02.01 mean- field shipped, 08.05.01 critical exponents shipped}; deepens both without duplicating.

Chapter structure. Adds two new sub-chapters to 08-stat-mech/:

08.10-thermodynamics/ — items 2, 13 (Maxwell relations, Clausius-Clapeyron). Optional alias 08.10-foundations/.
08.11-quantum-gases/ — items 3, 6, 8 (Bose-Fermi, Debye, van der Waals).
08.12-fluctuations/ — items 4, 9 (FDT, Einstein fluctuations).

Extends:

08.01-partition/ — item 1, 7 (microcanonical, Maxwell distribution).
08.02-mean-field/ — item 5 (Landau phenomenological theory).

Composite with shipped 22-unit chapter. Most efficient production order: because the 22-unit shipped chapter is field-theoretic-RG heavy, the Landau Vol 5 punch-list is purely complementary — no re-production of mean-field-Onsager-Wilson-Fisher-Wick-lattice- gauge material. The 9 new units of priority-1+2 (items 1–9) plus 3 deepenings of existing units = ~30% overlap with shipped Codex content, ~70% net-new physicist-thermodynamics material.

Apex unit designations. Items 4 and 5 are both apex units (originator-prose, paraphrasing Landau-Lifshitz 1957 §125 and Landau 1937 directly). Item 1 is near-apex for the Gibbs-1902 microcanonical sequencing (foundational across the chapter but not originator-prose-mandatory). All three warrant extended budget (5–6 h each rather than the typical 3.5 h).

§5 What this plan does NOT cover

Quantum statistical mechanics in a QFT sense. Landau Vol 5 stops at quantum statistics for distinguishable / Bose / Fermi particles on configuration-space wavefunctions; thermal field theory is FT 2.13 (Itzykson-Drouffe Statistical Field Theory). Codex 08.05–08.09 material — Wilson-Fisher RG, conformal criticality, lattice gauge — is already shipped and not duplicated.
Superfluidity and Bose / Fermi liquids. Deferred to Vol 9 Statistical Physics, Part 2 (not on Fast Track at present). Ideal-gas BEC is in scope (item 3 Master); the Landau two-fluid model and roton spectrum are out of scope.
Non-equilibrium kinetic theory. Deferred to Vol 10 Physical Kinetics (not on FT). Boltzmann equation, transport coefficients out of scope.
Critical-phenomena Wilson RG and ε-expansion. Already shipped in 08.04-rg/ and is the territory of FT 2.13 Itzykson-Drouffe (Goldenfeld serves as bridge text at FT 2.09). This audit references Landau-Ginzburg as the predecessor but does not duplicate the RG treatment.
Critical-phenomena RG as a separate FT entry. Critical-phenomena RG belongs to FT 2.13 Itzykson-Drouffe and its dedicated audit plan; this plan stays on the Landau Vol 5 side of the bridge.
Measure-theoretic / rigorous statistical mechanics. Ruelle, Israel, Lanford, Dobrushin are not in Landau's territory and not in scope. If a future FT entry adds a rigorous statistical-mechanics text (Friedli-Velenik Statistical Mechanics of Lattice Systems), separate audit.
Line-number Problem inventory. Landau's ~250 Problems form a separate per-section problem corpus. Inventory deferred under the reduced-audit constraint.
Russian original. Translation differences (Sykes-Kearsley vs. Russian) not catalogued; physicist-conventions track the English edition. Pre-1989 Soviet text — copyright nontrivial; English edition remains commercial.
Statistical Physics Part 2 (Vol 9). Not a FT entry; if added later, separate plan covering Bose / Fermi liquids, BCS superconductivity, hydrodynamic fluctuations.

§6 Acceptance criteria for FT equivalence (Landau Vol 5)

Per docs/plans/FASTTRACK_EQUIVALENCE_PLAN.md §3.4 and §9, Statistical Physics, Part 1 is at equivalence-coverage when:

≥95% of Landau's named results (and worked formulae) in Chapters I–IX, XII, XIV map to Codex units at Landau-equivalent pedagogical depth (currently ~30%; after priority-1 ~55%; after priority-1+2 ~80%; after priority-1+2+3 ~90%; after priority-4 ~95%). Items 4 (FDT), 5 (Landau 1937 phenomenological theory), and 3 (quantum gases) are the highest-leverage individual gaps.
≥80% of Landau's Problems have a Codex equivalent worked example (currently ~10%; closing requires a dedicated Landau-Vol-5- problem-pack pass — analogous to the proposed Vol 1 pass — out of scope for this audit).
≥90% of Landau's worked examples appear in a unit (currently ~10%; priority-1+2 brings to ~70%; remainder needs dedicated worked- example densification).
Notation crosswalk pinned in Master sections per §4. No standalone notation/landau-vol-5.md needed (the per-unit Master-tier paragraphs suffice).
DAG: for every microcanonical → canonical → grand-canonical → ideal gas → Bose/Fermi gas chain in Landau Chs. I–V, an unbroken prerequisite chain in Codex's DAG. Currently breaks at 08.01.05 (microcanonical) — item 1 closes it.
Pass-W weaving connects new units to existing 08.01-*, 08.02-*, 08.05-*, 08.06-*, and laterally to 05.02.07 Liouville Vol 1 (Hamiltonian mechanics → statistical mechanics).
Originator-prose units shipped: items 4 (08.12.01 FDT) and 5 (08.02.04 Landau 1937) both require explicit paraphrase of Landau-Lifshitz primary sources with [ref:] citations.

Reduced-audit caveat. Per AGENTIC_EXECUTION_PLAN.md §6.6 hard rule, P5 verification cannot mark Landau Vol 5 as equivalence-covered until a full audit replaces this reduced one (PDF acquired or canonical local TOC inventory at section-by- section depth). The reduced status applies even if all 13 punch-list items ship.

Prerequisite alert. Landau Vol 5 sits at FT 2.10 — after the Section 1 mathematics + classical-mechanics anchors (Apostol Vols I–II, Lang, Landau Vol 1 mechanics, Arnold MM, Landau Vol 2 Classical Fields, Cannas symplectic). Codex must keep the QM-foundations chain intact: introductory probability / measure theory (currently in 00-foundations and 04-analysis) must be present for items 1, 2, 4, 9; Landau Vol 1 §46 Liouville (already shipped at 05.02.07-liouville-volume) is lateral-cited from item 1. This Landau Vol 5 plan does not re-audit those prerequisites.

Honest scope. Mid-sized equivalence gap. The Codex 08-stat-mech/ chapter is mature on the field-theoretic / RG side (22 units shipped, of which 7 are at Landau-equivalent depth on shared topics: partition function, free energy, Boltzmann distribution, Ising, mean-field, critical exponents, spontaneous symmetry breaking) — but the Landau-canonical physicist- thermodynamics + fluctuations + worked-example layer (microcanonical sequencing, Maxwell relations, Bose/Fermi gases, Debye, fluctuation- dissipation, Landau 1937 phenomenological theory, van der Waals) is substantially uncaptured. Priority-1+2 batch is 9 new units + 3 deepenings — comparable to the Landau Vol 1 batch in scope but with a different center of mass (Vol 1 added Lagrangian-physics worked examples; Vol 5 adds physicist-thermodynamics + fluctuation / FDT / Landau-phase-transition material).

§7 Sourcing

Status: BUY per docs/catalogs/FASTTRACK_BOOKLIST.md.
Local copy: NOT RESOLVED. reference/textbooks-extra/ holds Vols 1, 2, 6, 8 of the Course of Theoretical Physics but not Vol 5. This is the dominant factor making the audit reduced. Recommended remediation: acquire a personal copy (legal Pergamon / Butterworth-Heinemann edition) or scan into reference/textbooks-extra/ as Vol 5 - Landau, Lifshitz - Statistical Physics Part 1 (3rd ed, 1980).pdf to mirror the Vol 1 / Vol 2 / Vol 6 / Vol 8 pattern. Promote audit to full after.
WebFetch fallback under the 3-hour budget: not pursued in this pass — the section-by-section TOC of Vol 5 is stable across all editions since 1958 and is reproduced in detail in all four peer sources cited below, which is sufficient for a reduced plan stub. A subsequent full audit pass should pull the PDF if a legal source is available.
Citation form: L. D. Landau, E. M. Lifshitz, Statistical Physics, Part 1, 3rd ed., revised and enlarged by E. M. Lifshitz and L. P. Pitaevskii, translated from the Russian by J. B. Sykes and M. J. Kearsley, Course of Theoretical Physics Volume 5 (Pergamon / Butterworth-Heinemann, Oxford, 1980; reprinted continuously). ISBN 0 7506 3372 7.
Russian original: Statisticheskaya Fizika, Nauka, Moscow, 1937 (1st); 1951 (2nd); 1964 (3rd); 1976 (4th). Pre-1989 Soviet text — copyright nontrivial; English Pergamon / Butterworth edition remains commercial.
Peer sources cited in this audit (peer-anchors for §1, ≥3 required):
- F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965; reprinted Waveland 2009) — American undergraduate physicist-thermodynamics canonical companion to Landau; treats microcanonical-first like Landau but at greater pedagogical density.
- M. Kardar, Statistical Physics of Particles (Cambridge UP, 2007) — graduate-level companion; Vol I (Particles) parallels Landau Vol 5 directly chapter-by-chapter at MIT graduate level. Most direct modern equivalent.
- N. Goldenfeld, Lectures on Phase Transitions and the Renormalization Group (Westview / Frontiers in Physics, 1992) — modern bridge text between Landau-Ginzburg phenomenological theory and Wilson-Fisher RG; cites Landau 1937 as originator and reproduces the Ginzburg criterion in detail. The canonical reference for items 5 and 11.
- R. K. Pathria, P. D. Beale, Statistical Mechanics, 3rd ed. (Academic Press / Elsevier, 2011) — comprehensive physicist reference; treats both microcanonical-first and partition- function-first sequencings; covers virial expansion and Bose-Einstein condensation at the same depth as Landau.
Additional originator references (cited in §3 punch-list): J. W. Gibbs, Elementary Principles in Statistical Mechanics (Yale UP, 1902); J. W. Gibbs, "On the Equilibrium of Heterogeneous Substances" (Trans. Conn. Acad. Arts Sci. 3:108, 343 (1875–78)); J. C. Maxwell, "Illustrations of the dynamical theory of gases" (Phil. Mag. 19:19 (1860)); L. Boltzmann, "Weitere Studien über das Wärmegleichgewicht unter Gasmolekülen" (Wien. Ber. 66:275 (1872)); A. Einstein, "Die Plancksche Theorie der Strahlung und die Theorie der spezifischen Wärme" (Ann. Phys. 22:180 (1907)); P. Debye, "Zur Theorie der spezifischen Wärmen" (Ann. Phys. 39:789 (1912)); S. N. Bose, "Plancks Gesetz und Lichtquanten- hypothese" (Z. Phys. 26:178 (1924)); A. Einstein, "Quantentheorie des einatomigen idealen Gases" (Sitz. Preuss. Akad. (1924)); E. Fermi, "Zur Quantelung des idealen einatomigen Gases" (Z. Phys. 36:902 (1926)); J. E. Mayer, "The statistical mechanics of condensing systems" (J. Chem. Phys. 5:67 (1937)); J. D. van der Waals, Over de Continuiteit van den Gas- en Vloeistoftoestand (Leiden, 1873); A. Einstein, "Theorie der Opaleszenz von homogenen Flüssigkeiten und Flüssigkeits- gemischen in der Nähe des kritischen Zustandes" (Ann. Phys. 33:1275 (1910)); H. Nyquist, "Thermal agitation of electric charge in conductors" (Phys. Rev. 32:110 (1928)); L. D. Landau, "On the theory of phase transitions" (Phys. Z. Sowjet. 11:26 (1937); Zh. Eksp. Teor. Fiz. 7:19 (1937)); L. D. Landau, E. M. Lifshitz, "Statistical fluctuations and generalized susceptibility" (Sov. Phys. JETP 5:512 (1957)); H. B. Callen, T. A. Welton, "Irreversibility and generalized noise" (Phys. Rev. 83:34 (1951)); R. Kubo, "Statistical- mechanical theory of irreversible processes I" (J. Phys. Soc. Japan 12:570 (1957)).
Local copy retention. If acquired in the future, store at reference/textbooks-extra/Vol 5 - Landau, Lifshitz - Statistical Physics Part 1 (3rd ed, 1980).pdf — mirroring the Vol 1 / 2 / 6 / 8 paths and not promoting into reference/fasttrack-texts/02-quantum-stat/, which is reserved for free-license / public-domain texts.

Landau, Lifshitz — *Statistical Physics, Part 1* (Fast Track 2.10) — Audit + Gap Plan