TauLib · API Book IV

TauLib.BookIV.ManyBody.DefectFunctionalExt2

TauLib.BookIV.ManyBody.DefectFunctionalExt2

Continuation of the many-body defect functional extension: fluid regime definitions (Euler, NS, MHD, plasma, superfluid, superconductor), temperature as defect gradient, phase transitions as regime crossings, and thermodynamic structure.

Registry Cross-References

  • [IV.D222] Euler Fluid Regime — EulerFluidRegime

  • [IV.P136] tau-Euler Equation — TauEulerEquation

  • [IV.D223] Navier-Stokes Regime — NavierStokesRegime

  • [IV.R161] Turbulence question — comment-only (conjectural)

  • [IV.D224] MHD Regime — MHDRegime

  • [IV.R162] MHD frozen flux — comment-only

  • [IV.D225] Plasma Regime — PlasmaRegime

  • [IV.D226] Superfluid Regime — SuperfluidRegime

  • [IV.P137] Superfluid Vortex Quantization — SuperfluidVortexQuantization

  • [IV.R163] Helium-4 and beyond — remark_helium4

  • [IV.D227] Superconductor Regime — SuperconductorRegime

  • [IV.P138] Flux Quantization — FluxQuantization

  • [IV.R164] Cooper pairing is topological — remark_cooper_pairing

  • [IV.R165] Regime table recap — comment-only

  • [IV.D228] Temperature as Defect Gradient — TemperatureAsDefectGradient

  • [IV.R166] Boltzmann constant status — comment-only

  • [IV.P139] Status of Boltzmann Constant — BoltzmannConstantStatus

  • [IV.R167] No intrinsic temperature scale — comment-only

  • [IV.T91] Second Law via Defect Functional — SecondLawViaDefect

  • [IV.R168] Arrow of time recap — comment-only

  • [IV.D229] First-order Phase Transition — FirstOrderTransition

  • [IV.D230] Second-order Phase Transition — SecondOrderTransition

  • [IV.T92] Phase Transition as Regime Crossing — PhaseTransitionRegimeCrossing

  • [IV.R169] Universality and critical exponents — remark_universality (conjectural)

Mathematical Content

This module completes ch52 by defining the fluid regimes as subsets of the defect tuple space D = R_{>=0} x R x R x Z, and establishing the thermodynamic structure: temperature as the defect gradient, the second law as defect-entropy non-decrease, and phase transitions as inequality crossings in the defect tuple.

Ground Truth Sources

  • Chapter 52 of Book IV (2nd Edition)

  • fluid-condensed-matter.json: regime classification, tau-superfluidity

Tau.BookIV.ManyBody.EulerFluidRegime

source structure Tau.BookIV.ManyBody.EulerFluidRegime :Type

[IV.D222] The Euler fluid regime: the subset of D where 0 < mu <= mu_crit and the Euler budget constraint holds: mu + nu + kappa + theta = const (inviscid, no dissipation).

Distinguished from the single-bundle Euler regime by including N-body interaction corrections in the budget law.

  • mobility_bounded : Bool Mobility bounded by critical threshold.

  • budget_conserved : Bool Budget conservation holds.

  • inviscid : Bool No dissipation (inviscid).

  • kelvin_holds : Bool Kelvin circulation theorem holds.

Instances For

Tau.BookIV.ManyBody.instReprEulerFluidRegime.repr

source def Tau.BookIV.ManyBody.instReprEulerFluidRegime.repr :EulerFluidRegime → ℕ → Std.Format

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Tau.BookIV.ManyBody.instReprEulerFluidRegime

source instance Tau.BookIV.ManyBody.instReprEulerFluidRegime :Repr EulerFluidRegime

Equations

  • Tau.BookIV.ManyBody.instReprEulerFluidRegime = { reprPrec := Tau.BookIV.ManyBody.instReprEulerFluidRegime.repr }

Tau.BookIV.ManyBody.euler_fluid_regime

source def Tau.BookIV.ManyBody.euler_fluid_regime :EulerFluidRegime

Equations

  • Tau.BookIV.ManyBody.euler_fluid_regime = { } Instances For

Tau.BookIV.ManyBody.TauEulerEquation

source structure Tau.BookIV.ManyBody.TauEulerEquation :Type

[IV.P136] In the Euler fluid regime the macroscopic defect tuple evolves as d/dn (mu_n, nu_n, kappa_n, theta_n) = (f_mu, f_nu, f_kappa, 0) subject to the budget constraint. The theta component has zero derivative because topological charge is a deformation invariant.

This is the tau-native formulation of the Euler equation.

  • theta_derivative_zero : Bool Theta derivative is zero.

  • budget_constraint : Bool Budget constraint enforced.

  • tau_native : Bool tau-native (no PDE imported).

Instances For

Tau.BookIV.ManyBody.instReprTauEulerEquation.repr

source def Tau.BookIV.ManyBody.instReprTauEulerEquation.repr :TauEulerEquation → ℕ → Std.Format

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Tau.BookIV.ManyBody.instReprTauEulerEquation

source instance Tau.BookIV.ManyBody.instReprTauEulerEquation :Repr TauEulerEquation

Equations

  • Tau.BookIV.ManyBody.instReprTauEulerEquation = { reprPrec := Tau.BookIV.ManyBody.instReprTauEulerEquation.repr }

Tau.BookIV.ManyBody.tau_euler_equation

source def Tau.BookIV.ManyBody.tau_euler_equation :TauEulerEquation

Equations

  • Tau.BookIV.ManyBody.tau_euler_equation = { } Instances For

Tau.BookIV.ManyBody.euler_theta_invariant

source theorem Tau.BookIV.ManyBody.euler_theta_invariant :tau_euler_equation.theta_derivative_zero = true

Tau.BookIV.ManyBody.NavierStokesRegime

source structure Tau.BookIV.ManyBody.NavierStokesRegime :Type

[IV.D223] The Navier-Stokes regime: mu > mu_crit, where the Euler budget is broken by viscous shear-defect dissipation. The budget decays monotonically, encoding energy dissipation.

The tau-NS equation is the evolution law in this regime.

  • above_threshold : Bool Mobility above critical threshold.

  • budget_broken : Bool Euler budget broken.

  • dissipative : Bool Dissipation present.

  • viscosity_derived : Bool Viscosity from defect geometry (not free parameter).

Instances For

Tau.BookIV.ManyBody.instReprNavierStokesRegime

source instance Tau.BookIV.ManyBody.instReprNavierStokesRegime :Repr NavierStokesRegime

Equations

  • Tau.BookIV.ManyBody.instReprNavierStokesRegime = { reprPrec := Tau.BookIV.ManyBody.instReprNavierStokesRegime.repr }

Tau.BookIV.ManyBody.instReprNavierStokesRegime.repr

source def Tau.BookIV.ManyBody.instReprNavierStokesRegime.repr :NavierStokesRegime → ℕ → Std.Format

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Tau.BookIV.ManyBody.ns_regime

source def Tau.BookIV.ManyBody.ns_regime :NavierStokesRegime

Equations

  • Tau.BookIV.ManyBody.ns_regime = { } Instances For

Tau.BookIV.ManyBody.MHDRegime

source structure Tau.BookIV.ManyBody.MHDRegime :Type

[IV.D224] The MHD (magnetohydrodynamic) regime: nu » mu and kappa is coupled to the B-sector. The system exhibits frozen-flux behavior (Alfven modes) where magnetic field lines move with the fluid.

EM holonomy is coupled to fluid transport.

  • vorticity_dominant : Bool Vorticity dominates mobility.

  • em_coupled : Bool B-sector coupled (EM holonomy).

  • frozen_flux : Bool Frozen-flux behavior.

  • alfven_modes : Bool Alfven modes present.

Instances For

Tau.BookIV.ManyBody.instReprMHDRegime.repr

source def Tau.BookIV.ManyBody.instReprMHDRegime.repr :MHDRegime → ℕ → Std.Format

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Tau.BookIV.ManyBody.instReprMHDRegime

source instance Tau.BookIV.ManyBody.instReprMHDRegime :Repr MHDRegime

Equations

  • Tau.BookIV.ManyBody.instReprMHDRegime = { reprPrec := Tau.BookIV.ManyBody.instReprMHDRegime.repr }

Tau.BookIV.ManyBody.mhd_regime

source def Tau.BookIV.ManyBody.mhd_regime :MHDRegime

Equations

  • Tau.BookIV.ManyBody.mhd_regime = { } Instances For

Tau.BookIV.ManyBody.PlasmaRegime

source structure Tau.BookIV.ManyBody.PlasmaRegime :Type

[IV.D225] The plasma regime: mu, |nu|, |kappa| > mu_crit and theta is fluctuating (not globally fixed). Topological charge can change through defect pair creation/annihilation.

  • all_above_threshold : Bool All transport components above threshold.

  • theta_fluctuating : Bool Theta fluctuating.

  • debye_screening : Bool Debye screening present.

Instances For

Tau.BookIV.ManyBody.instReprPlasmaRegime.repr

source def Tau.BookIV.ManyBody.instReprPlasmaRegime.repr :PlasmaRegime → ℕ → Std.Format

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Tau.BookIV.ManyBody.instReprPlasmaRegime

source instance Tau.BookIV.ManyBody.instReprPlasmaRegime :Repr PlasmaRegime

Equations

  • Tau.BookIV.ManyBody.instReprPlasmaRegime = { reprPrec := Tau.BookIV.ManyBody.instReprPlasmaRegime.repr }

Tau.BookIV.ManyBody.plasma_regime

source def Tau.BookIV.ManyBody.plasma_regime :PlasmaRegime

Equations

  • Tau.BookIV.ManyBody.plasma_regime = { } Instances For

Tau.BookIV.ManyBody.SuperfluidRegime

source structure Tau.BookIV.ManyBody.SuperfluidRegime :Type

[IV.D226] The superfluid regime: mu = mu_max (maximal mobility), nu = 0 a.e. (vanishing vorticity except at isolated quantized vortex cores), kappa = 0 (incompressible), theta quantized.

Transport is maximally free, rotation is suppressed except at topological defects with integer winding number.

  • maximal_mobility : Bool Maximal mobility.

  • vorticity_vanishes_ae : Bool Vorticity vanishes (except at cores).

  • incompressible : Bool Incompressible.

  • theta_quantized : Bool Theta quantized at vortex cores.

Instances For

Tau.BookIV.ManyBody.instReprSuperfluidRegime.repr

source def Tau.BookIV.ManyBody.instReprSuperfluidRegime.repr :SuperfluidRegime → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.instReprSuperfluidRegime

source instance Tau.BookIV.ManyBody.instReprSuperfluidRegime :Repr SuperfluidRegime

Equations

  • Tau.BookIV.ManyBody.instReprSuperfluidRegime = { reprPrec := Tau.BookIV.ManyBody.instReprSuperfluidRegime.repr }

Tau.BookIV.ManyBody.superfluid_regime

source def Tau.BookIV.ManyBody.superfluid_regime :SuperfluidRegime

Equations

  • Tau.BookIV.ManyBody.superfluid_regime = { } Instances For

Tau.BookIV.ManyBody.SuperfluidVortexQuantization

source structure Tau.BookIV.ManyBody.SuperfluidVortexQuantization :Type

[IV.P137] In the superfluid regime every vortex core carries theta_core in Z \ {0}, and the total circulation around any loop enclosing k cores is 2pihbar_tau/m times the sum of winding numbers.

Quantization is structural (from pi_1(T^2) = Z^2), not imposed.

  • charge_nonzero_integer : Bool Vortex charge is nonzero integer.

  • circulation_quantized : Bool Circulation quantized.

  • structural_origin : String Structural origin: pi_1(T^2).

Instances For

Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization

source instance Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization :Repr SuperfluidVortexQuantization

Equations

  • Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization = { reprPrec := Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization.repr }

Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization.repr

source def Tau.BookIV.ManyBody.instReprSuperfluidVortexQuantization.repr :SuperfluidVortexQuantization → ℕ → Std.Format

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Tau.BookIV.ManyBody.superfluid_vortex_quant

source def Tau.BookIV.ManyBody.superfluid_vortex_quant :SuperfluidVortexQuantization

Equations

  • Tau.BookIV.ManyBody.superfluid_vortex_quant = { } Instances For

Tau.BookIV.ManyBody.remark_helium4

source def Tau.BookIV.ManyBody.remark_helium4 :String

[IV.R163] In orthodox physics, superfluid He-4 has quantized circulation h/m_{He}. In Category tau the quantization is structural: it follows from the integer-valued topological charge on T^2. Equations

  • Tau.BookIV.ManyBody.remark_helium4 = “He-4: h/m_He quantization; in tau: structural from Z-valued theta on T^2” Instances For

Tau.BookIV.ManyBody.SuperconductorRegime

source structure Tau.BookIV.ManyBody.SuperconductorRegime :Type

[IV.D227] The superconductor regime: B-sector mobility mu_B = mu_max, theta in Z (quantized), and magnetic flux is quantized in units of Phi_0 = h/(2e). The Meissner effect (flux expulsion) follows from the B-sector superfluid structure.

  • b_sector_maximal : Bool B-sector maximal mobility.

  • theta_quantized : Bool Topological charge quantized.

  • flux_quantized : Bool Magnetic flux quantized.

  • meissner : Bool Meissner effect from B-sector superfluid.

Instances For

Tau.BookIV.ManyBody.instReprSuperconductorRegime

source instance Tau.BookIV.ManyBody.instReprSuperconductorRegime :Repr SuperconductorRegime

Equations

  • Tau.BookIV.ManyBody.instReprSuperconductorRegime = { reprPrec := Tau.BookIV.ManyBody.instReprSuperconductorRegime.repr }

Tau.BookIV.ManyBody.instReprSuperconductorRegime.repr

source def Tau.BookIV.ManyBody.instReprSuperconductorRegime.repr :SuperconductorRegime → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.superconductor_regime

source def Tau.BookIV.ManyBody.superconductor_regime :SuperconductorRegime

Equations

  • Tau.BookIV.ManyBody.superconductor_regime = { } Instances For

Tau.BookIV.ManyBody.FluxQuantization

source structure Tau.BookIV.ManyBody.FluxQuantization :Type

[IV.P138] Flux quantization from topological charge: in the superconductor regime, the integrality of theta on T^2 implies magnetic flux through any closed surface is quantized: Phi = n * Phi_0, n in Z.

This is the structural origin of the Abrikosov vortex lattice.

  • quantized : Bool Flux = n * Phi_0.

  • origin : String Origin: theta integrality on T^2.

  • abrikosov : Bool Consequence: Abrikosov vortex lattice.

Instances For

Tau.BookIV.ManyBody.instReprFluxQuantization

source instance Tau.BookIV.ManyBody.instReprFluxQuantization :Repr FluxQuantization

Equations

  • Tau.BookIV.ManyBody.instReprFluxQuantization = { reprPrec := Tau.BookIV.ManyBody.instReprFluxQuantization.repr }

Tau.BookIV.ManyBody.instReprFluxQuantization.repr

source def Tau.BookIV.ManyBody.instReprFluxQuantization.repr :FluxQuantization → ℕ → Std.Format

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Tau.BookIV.ManyBody.flux_quantization

source def Tau.BookIV.ManyBody.flux_quantization :FluxQuantization

Equations

  • Tau.BookIV.ManyBody.flux_quantization = { } Instances For

Tau.BookIV.ManyBody.remark_cooper_pairing

source def Tau.BookIV.ManyBody.remark_cooper_pairing :String

[IV.R164] Cooper pairing is topological: two electron defect bundles with opposite momentum share a combined T^2 character with even winding number, forming a bosonic composite. Equations

  • Tau.BookIV.ManyBody.remark_cooper_pairing = “Cooper pairs: opposite momentum, combined even theta, bosonic composite” Instances For

Tau.BookIV.ManyBody.TemperatureAsDefectGradient

source structure Tau.BookIV.ManyBody.TemperatureAsDefectGradient :Type

[IV.D228] The tau-temperature T_tau(C) = d deltaomega / d S_def(C) is the gradient of the universal defect functional with respect to defect entropy. It is a structural quantity, not an empirical postulate.

  • definition : String Definition: gradient of delta w.r.t. S_def.

  • structural : Bool Structural (not empirical).

  • nonneg : Bool Non-negative (mobility >= 0 implies T_tau >= 0).

Instances For

Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient

source instance Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient :Repr TemperatureAsDefectGradient

Equations

  • Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient = { reprPrec := Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient.repr }

Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient.repr

source def Tau.BookIV.ManyBody.instReprTemperatureAsDefectGradient.repr :TemperatureAsDefectGradient → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.temperature_defect_gradient

source def Tau.BookIV.ManyBody.temperature_defect_gradient :TemperatureAsDefectGradient

Equations

  • Tau.BookIV.ManyBody.temperature_defect_gradient = { } Instances For

Tau.BookIV.ManyBody.BoltzmannConstantStatus

source structure Tau.BookIV.ManyBody.BoltzmannConstantStatus :Type

[IV.P139] The Boltzmann constant k_B is an SI conversion factor, not an ontic tau-constant. It converts dimensionless tau-temperature to kelvin. In the tau-framework temperature is already dimensionless.

  • is_conversion_factor : Bool k_B is a conversion factor.

  • not_ontic : Bool Not an ontic constant.

  • tau_temp_dimensionless : Bool tau-temperature is dimensionless.

Instances For

Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus

source instance Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus :Repr BoltzmannConstantStatus

Equations

  • Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus = { reprPrec := Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus.repr }

Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus.repr

source def Tau.BookIV.ManyBody.instReprBoltzmannConstantStatus.repr :BoltzmannConstantStatus → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.boltzmann_status

source def Tau.BookIV.ManyBody.boltzmann_status :BoltzmannConstantStatus

Equations

  • Tau.BookIV.ManyBody.boltzmann_status = { } Instances For

Tau.BookIV.ManyBody.boltzmann_is_conversion

source theorem Tau.BookIV.ManyBody.boltzmann_is_conversion :boltzmann_status.is_conversion_factor = true

Tau.BookIV.ManyBody.SecondLawViaDefect

source structure Tau.BookIV.ManyBody.SecondLawViaDefect :Type

[IV.T91] Second law via defect functional: under propagation Phi_{n,n+1}, defect entropy S_def is non-increasing, refinement entropy S_ref is non-decreasing, and total entropy S = S_def + S_ref is non-decreasing. This is the structural second law of thermodynamics.

The arrow of time is the direction of increasing S_ref.

  • s_def_nonincreasing : Bool S_def non-increasing.

  • s_ref_nondecreasing : Bool S_ref non-decreasing.

  • s_total_nondecreasing : Bool S_total = S_def + S_ref non-decreasing.

  • arrow_of_time : String Arrow of time: direction of increasing S_ref.

Instances For

Tau.BookIV.ManyBody.instReprSecondLawViaDefect.repr

source def Tau.BookIV.ManyBody.instReprSecondLawViaDefect.repr :SecondLawViaDefect → ℕ → Std.Format

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Tau.BookIV.ManyBody.instReprSecondLawViaDefect

source instance Tau.BookIV.ManyBody.instReprSecondLawViaDefect :Repr SecondLawViaDefect

Equations

  • Tau.BookIV.ManyBody.instReprSecondLawViaDefect = { reprPrec := Tau.BookIV.ManyBody.instReprSecondLawViaDefect.repr }

Tau.BookIV.ManyBody.second_law_defect

source def Tau.BookIV.ManyBody.second_law_defect :SecondLawViaDefect

Equations

  • Tau.BookIV.ManyBody.second_law_defect = { } Instances For

Tau.BookIV.ManyBody.second_law_total_nondecreasing

source theorem Tau.BookIV.ManyBody.second_law_total_nondecreasing :second_law_defect.s_total_nondecreasing = true

Tau.BookIV.ManyBody.FirstOrderTransition

source structure Tau.BookIV.ManyBody.FirstOrderTransition :Type

[IV.D229] A first-order phase transition at defect entropy S_0 is a discontinuity in the tau-temperature: lim_{S->S_0^-} T_tau(S) is different from lim_{S->S_0^+} T_tau(S). The defect tuple jumps discontinuously across a regime boundary.

  • temp_discontinuous : Bool Temperature discontinuity.

  • tuple_jumps : Bool Defect tuple jumps.

  • has_latent_heat : Bool Latent heat = jump magnitude.

Instances For

Tau.BookIV.ManyBody.instReprFirstOrderTransition.repr

source def Tau.BookIV.ManyBody.instReprFirstOrderTransition.repr :FirstOrderTransition → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.instReprFirstOrderTransition

source instance Tau.BookIV.ManyBody.instReprFirstOrderTransition :Repr FirstOrderTransition

Equations

  • Tau.BookIV.ManyBody.instReprFirstOrderTransition = { reprPrec := Tau.BookIV.ManyBody.instReprFirstOrderTransition.repr }

Tau.BookIV.ManyBody.first_order_transition

source def Tau.BookIV.ManyBody.first_order_transition :FirstOrderTransition

Equations

  • Tau.BookIV.ManyBody.first_order_transition = { } Instances For

Tau.BookIV.ManyBody.SecondOrderTransition

source structure Tau.BookIV.ManyBody.SecondOrderTransition :Type

[IV.D230] A second-order (continuous) phase transition at S_0 is a point where T_tau is continuous but dT_tau/dS_def is discontinuous. The defect tuple is continuous but its derivative jumps.

  • temp_continuous : Bool Temperature continuous.

  • deriv_discontinuous : Bool Temperature derivative discontinuous.

  • no_latent_heat : Bool No latent heat.

Instances For

Tau.BookIV.ManyBody.instReprSecondOrderTransition.repr

source def Tau.BookIV.ManyBody.instReprSecondOrderTransition.repr :SecondOrderTransition → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.instReprSecondOrderTransition

source instance Tau.BookIV.ManyBody.instReprSecondOrderTransition :Repr SecondOrderTransition

Equations

  • Tau.BookIV.ManyBody.instReprSecondOrderTransition = { reprPrec := Tau.BookIV.ManyBody.instReprSecondOrderTransition.repr }

Tau.BookIV.ManyBody.second_order_transition

source def Tau.BookIV.ManyBody.second_order_transition :SecondOrderTransition

Equations

  • Tau.BookIV.ManyBody.second_order_transition = { } Instances For

Tau.BookIV.ManyBody.PhaseTransitionRegimeCrossing

source structure Tau.BookIV.ManyBody.PhaseTransitionRegimeCrossing :Type

[IV.T92] Every phase transition is an inequality crossing in D: first-order transitions correspond to the defect tuple jumping discontinuously from one regime to another, second-order transitions to the tuple arriving at a regime boundary continuously.

There are no “exotic” phase transitions outside this classification.

  • first_order_discontinuous : Bool First-order: discontinuous crossing.

  • second_order_continuous : Bool Second-order: continuous crossing.

  • complete_classification : Bool No exotic transitions outside classification.

  • all_are_regime_crossings : Bool All transitions are regime crossings in D.

Instances For

Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing.repr

source def Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing.repr :PhaseTransitionRegimeCrossing → ℕ → Std.Format

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  • One or more equations did not get rendered due to their size. Instances For

Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing

source instance Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing :Repr PhaseTransitionRegimeCrossing

Equations

  • Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing = { reprPrec := Tau.BookIV.ManyBody.instReprPhaseTransitionRegimeCrossing.repr }

Tau.BookIV.ManyBody.phase_transition_crossing

source def Tau.BookIV.ManyBody.phase_transition_crossing :PhaseTransitionRegimeCrossing

Equations

  • Tau.BookIV.ManyBody.phase_transition_crossing = { } Instances For

Tau.BookIV.ManyBody.all_transitions_are_crossings

source theorem Tau.BookIV.ManyBody.all_transitions_are_crossings :phase_transition_crossing.all_are_regime_crossings = true

Tau.BookIV.ManyBody.remark_universality

source def Tau.BookIV.ManyBody.remark_universality :String

[IV.R169] (Conjectural) Universality and critical exponents: Critical exponents of Landau-Ginzburg/Wilson-Fisher theory are readout-level quantities determined by the defect-tuple geometry near the regime boundary. Scope: conjectural. Equations

  • Tau.BookIV.ManyBody.remark_universality = “[conjectural] Critical exponents from defect-tuple geometry near “ ++ “regime boundaries; readout-level, not ontic” Instances For