recognition /
Thermodynamics /
Thermodynamics.PartitionFunction /
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formal statement (Lean)
42 structure DiscreteSystem where
43 /-- Number of energy levels -/
44 numLevels : ℕ
45 /-- Energy of each level -/
46 energy : Fin numLevels → ℝ
47 /-- Degeneracy of each level (must be positive) -/
48 degeneracy : Fin numLevels → ℕ
49 /-- At least one level -/
50 nonempty : numLevels > 0
51 /-- Each level has degeneracy ≥ 1 -/
52 deg_pos : ∀ i, degeneracy i ≥ 1
53
54 /-- The canonical partition function Z = Σᵢ gᵢ exp(-βEᵢ). -/
used by (6)
From the project-wide theorem graph. These declarations reference this one in their body.
averageEnergy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
entropy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
freeEnergy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
heatCapacity
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
partitionFunction
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
partition_function_positive
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
depends on (16)
Lean names referenced from this declaration's body.
of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
decl_use
Energy
in IndisputableMonolith.Constants.RSNativeUnits
decl_use
has
in IndisputableMonolith.Engineering.AsteroidOreSpectroscopy
decl_use
canonical
in IndisputableMonolith.Foundation.ArithmeticOf
decl_use
of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
one
in IndisputableMonolith.Foundation.IntegersFromLogic
decl_use
of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
one
in IndisputableMonolith.Foundation.RationalsFromLogic
decl_use
of
in IndisputableMonolith.Foundation.SpectralEmergence
decl_use
canonical
in IndisputableMonolith.Gap45.Beat
decl_use
of
in IndisputableMonolith.Information.PhysicsComplexityStructure
decl_use
Z
in IndisputableMonolith.Masses.Anchor
decl_use
canonical
in IndisputableMonolith.NavierStokes.RM2U.NonParasitism
decl_use
Z
in IndisputableMonolith.Physics.AnchorPolicyCertified
decl_use
one
in IndisputableMonolith.QFT.SpinStatistics
decl_use
one
in IndisputableMonolith.RecogSpec.Core
decl_use