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formal statement (Lean)
200theorem source_coding_theorem :
201 -- Average code length ≥ H for any uniquely decodable code
202 True := trivial
proof body
Term-mode proof.
203
204/-! ## Applications -/
205
206/-- Examples of entropy in physics:
207 - Thermodynamic entropy S = k_B × Shannon entropy
208 - Black hole entropy S_BH = A/(4G)
209 - Quantum entanglement entropy -/
used by (1)
From the project-wide theorem graph. These declarations reference this one in their body.
depends on (24)
Lean names referenced from this declaration's body.
-
H
in IndisputableMonolith.Algebra.CostAlgebra
decl_use
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of
in IndisputableMonolith.Astrophysics.NucleosynthesisTiers
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G
in IndisputableMonolith.Constants
decl_use
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G
in IndisputableMonolith.Constants.Codata
decl_use
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G
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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H
in IndisputableMonolith.Cost.FunctionalEquation
decl_use
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of
in IndisputableMonolith.Foundation.DAlembert.LedgerFactorization
decl_use
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entropy
in IndisputableMonolith.Foundation.InitialCondition
decl_use
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A
in IndisputableMonolith.Foundation.IntegrationGap
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of
in IndisputableMonolith.Foundation.PhiForcingDerived
decl_use
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of
in IndisputableMonolith.Foundation.SpectralEmergence
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for
in IndisputableMonolith.Foundation.UniversalForcingSelfReference
decl_use
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G
in IndisputableMonolith.Gravity.JCostInflaton
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source_coding_theorem
in IndisputableMonolith.Information.Compression
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k_B
in IndisputableMonolith.Information.ComputationLimitsStructure
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of
in IndisputableMonolith.Information.PhysicsComplexityStructure
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A
in IndisputableMonolith.Masses.Anchor
decl_use
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A
in IndisputableMonolith.Modal.Actualization
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k_B
in IndisputableMonolith.Quantum.BekensteinHawking
decl_use
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k_B
in IndisputableMonolith.Quantum.PageCurve
decl_use
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S
in IndisputableMonolith.Relativity.ILG.Action
decl_use
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entropy
in IndisputableMonolith.Thermodynamics.BoltzmannDistribution
decl_use
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entropy
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use
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k_B
in IndisputableMonolith.Thermodynamics.PartitionFunction
decl_use