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Thermodynamics /
Thermodynamics.PartitionFunction /
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formal statement (Lean)
188 theorem classical_limit :
189 -- As T → ∞ and states become dense:
190 -- Σ → ∫ d³q d³p / h³
191 -- This is Liouville's phase space measure
192 True := trivial
proof body
Term-mode proof.
193
194 /-! ## Quantum Statistics -/
195
196 /-- For indistinguishable particles, we need:
197
198 **Fermions**: Fermi-Dirac distribution (odd 8-tick phase)
199 Z_FD = Π_k (1 + exp(-β(E_k - μ)))
200
201 **Bosons**: Bose-Einstein distribution (even 8-tick phase)
202 Z_BE = Π_k (1 - exp(-β(E_k - μ)))⁻¹ -/
used by (2)
From the project-wide theorem graph. These declarations reference this one in their body.
classical_limit
in IndisputableMonolith.Thermodynamics.BoseEinstein
decl_use
classical_limit
in IndisputableMonolith.Thermodynamics.FermiDirac
decl_use
depends on (14)
Lean names referenced from this declaration's body.
tick
in IndisputableMonolith.Constants
decl_use
tick
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
T
in IndisputableMonolith.Foundation.Breath1024
decl_use
phase
in IndisputableMonolith.Foundation.EightTick
decl_use
is
in IndisputableMonolith.Foundation.OptionAEmpiricalProgram
decl_use
is
in IndisputableMonolith.Foundation.SimplicialLedger.EdgeLengthFromPsi
decl_use
is
in IndisputableMonolith.GameTheory.MechanismDesignFromSigma
decl_use
T
in IndisputableMonolith.Gap45.SyncMinimization
decl_use
is
in IndisputableMonolith.Mathematics.RamanujanBridge.MockThetaPhantom
decl_use
and
in IndisputableMonolith.NumberTheory.CirclePhaseLift
decl_use
phase
in IndisputableMonolith.NumberTheory.RiemannHypothesis.Wedge
decl_use
Statistics
in IndisputableMonolith.QFT.SpinStatistics
decl_use
classical_limit
in IndisputableMonolith.Thermodynamics.BoseEinstein
decl_use
classical_limit
in IndisputableMonolith.Thermodynamics.FermiDirac
decl_use