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formal statement (Lean)
75noncomputable def freeEnergy (sys : DiscreteSystem) (T : ℝ) (hT : T > 0) : ℝ :=
proof body
Definition body.
76 -k_B * T * log (partitionFunction sys T hT)
77
78/-- Average energy ⟨E⟩ = -∂ln Z/∂β = Σᵢ Eᵢ Pᵢ. -/
used by (3)
From the project-wide theorem graph. These declarations reference this one in their body.
-
freeEnergy
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
-
free_energy_identity
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
-
freeEnergy
in IndisputableMonolith.Thermodynamics.JCostThermoBridge
decl_use
depends on (16)
Lean names referenced from this declaration's body.
-
T
in IndisputableMonolith.Foundation.Breath1024
decl_use
-
E
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
-
T
in IndisputableMonolith.Gap45.SyncMinimization
decl_use
-
k_B
in IndisputableMonolith.Information.ComputationLimitsStructure
decl_use
-
Z
in IndisputableMonolith.Masses.Anchor
decl_use
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Z
in IndisputableMonolith.Physics.AnchorPolicyCertified
decl_use
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k_B
in IndisputableMonolith.Quantum.BekensteinHawking
decl_use
-
k_B
in IndisputableMonolith.Quantum.PageCurve
decl_use
-
freeEnergy
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
-
partitionFunction
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
-
partitionFunction
in IndisputableMonolith.Thermodynamics.HelmholtzReal
decl_use
-
freeEnergy
in IndisputableMonolith.Thermodynamics.JCostThermoBridge
decl_use
-
partitionFunction
in IndisputableMonolith.Thermodynamics.JCostThermoBridge
decl_use
-
DiscreteSystem
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
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k_B
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
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partitionFunction
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use